We are given: sinθ = x and secθ = y. Step 1: Recall the trigonometric identities 1. The definition of secθ is: secθ = 1/cosθ. Therefore, cosθ = 1/secθ = 1/y. 2. The definition of tanθ is: tanθ = sinθ / cosθ. Step 2: Substitute the values of sinθ and cosθ From the problem, sinθ = x and cosθ = 1/y. SuRead more
We are given:
sinθ = x and secθ = y.
Step 1: Recall the trigonometric identities
1. The definition of secθ is:
secθ = 1/cosθ.
Therefore, cosθ = 1/secθ = 1/y.
2. The definition of tanθ is:
tanθ = sinθ / cosθ.
Step 2: Substitute the values of sinθ and cosθ
From the problem, sinθ = x and cosθ = 1/y. Substituting these into the formula for tanθ:
tanθ = sinθ / cosθ
= x / (1/y)
Step 3: Simplify the expression
Dividing by 1/y is equivalent to multiplying by y:
tanθ = x * y
= xy
Step 4: Final Answer
Thus, tanθ is equal to xy.
The correct answer is:
a) xy
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
We are given the equation: 5 tanθ - 4 = 0. Step 1: Solve for tanθ Rearrange the equation to solve for tanθ: 5 tanθ = 4 tanθ = 4/5. Step 2: Express sinθ and cosθ in terms of tanθ Using the identity tanθ = sinθ / cosθ, we can write: sinθ = 4k and cosθ = 5k, where k is a positive constant such that sinRead more
We are given the equation:
5 tanθ – 4 = 0.
Step 1: Solve for tanθ
Rearrange the equation to solve for tanθ:
5 tanθ = 4
tanθ = 4/5.
Step 2: Express sinθ and cosθ in terms of tanθ
Using the identity tanθ = sinθ / cosθ, we can write:
sinθ = 4k and cosθ = 5k,
where k is a positive constant such that sin²θ + cos²θ = 1 (Pythagorean identity).
Substitute sinθ = 4k and cosθ = 5k into the identity:
(4k)² + (5k)² = 1
16k² + 25k² = 1
41k² = 1
k² = 1/41
k = √(1/41).
Thus:
sinθ = 4k = 4/√41,
cosθ = 5k = 5/√41.
Step 3: Simplify the given expression
We are tasked with finding the value of:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ).
Substitute sinθ = 4/√41 and cosθ = 5/√41 into the expression:
Step 4: Final Answer
The value of the given expression is 0.
The correct answer is:
c) zero
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
To determine how many linear equations in x and y can be satisfied by x=1 and y=2, let's analyze the situation. A linear equation in x and y typically has the form: Ax+By=C where A, B and C are constants. For a given pair ( x = 1, y= 2), we can substitute these values into the equation to see if itRead more
To determine how many linear equations in x and y can be satisfied by x=1 and y=2, let’s analyze the situation.
A linear equation in x and y typically has the form: Ax+By=C
where A, B and C are constants. For a given pair ( x = 1, y= 2), we can substitute these values into the equation to see if it holds.
Step 1: Substitute x=1 and y=2 into the general form of the equation Ax + By = C:
A(1) + B(2) = C
A + 2B = C
This equation can be true from many different values of A, B and C. So, there is not just one equation, but many possible equations that can be formed depending on the values of A and B.
Step 2: General conclusion
There is no unique solution for the values of A, B and C. This means infinitely many linear equations can be satisfied by the point (x=1,y=2).
Conclusion:
The correct answer is (c) infinitely many.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
A linear equation in two variables has infinitely many solutions, provided that the equation represents a line in a two-dimensional plane. A linear equation in two variables typically has the form: ax + by = c where a, b, and c are constants. This equation represents a straight line on a coordinateRead more
A linear equation in two variables has infinitely many solutions, provided that the equation represents a line in a two-dimensional plane.
A linear equation in two variables typically has the form: ax + by = c
where a, b, and c are constants. This equation represents a straight line on a coordinate plane, and every point on this line is a solution to the equation.
Infinitely many solutions: Since a straight line has infinitely many points, the equation has infinitely many solutions, as each point on the line represents a valid pair of values for x and y.
Conclusion:
The correct answer is (d) infinitely many solutions.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
The solution of a linear equation in two variables is an ordered pair (x,y) that satisfies the equation when the values of x and y are substituted into the equation. Explanation: A linear equation in two variables typically has the form ax+by=c, where a, b, and c are constants, and x and y are the vRead more
The solution of a linear equation in two variables is an ordered pair (x,y) that satisfies the equation when the values of x and y are substituted into the equation.
Explanation:
A linear equation in two variables typically has the form ax+by=c, where a, b, and c are constants, and x and y are the variables. The solution is the set of values x and y (an ordered pair) that, when substituted into the equation, make the equation true.
Option (a): a number which satisfies the given equation
This is not correct because the solution is not just a single number but an ordered pair of numbers. So, (a) is incorrect.
Option (b): an ordered pair which satisfies the given equation
This is partially correct, but it’s a bit incomplete because it doesn’t clarify that the ordered pair is specific to the equation and needs to satisfy the equation. (b) is incomplete.
Option (c): an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it
This is the most accurate description. The solution is indeed an ordered pair, and when the values of x and y are substituted into the equation, the equation must be satisfied. (c) is correct.
Option (d): none of these
Since option (c) is correct, this option is incorrect. (d) is incorrect.
Conclusion: The correct answer is (c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
If sinθ = x and secθ = y, then tanθ is equal to
We are given: sinθ = x and secθ = y. Step 1: Recall the trigonometric identities 1. The definition of secθ is: secθ = 1/cosθ. Therefore, cosθ = 1/secθ = 1/y. 2. The definition of tanθ is: tanθ = sinθ / cosθ. Step 2: Substitute the values of sinθ and cosθ From the problem, sinθ = x and cosθ = 1/y. SuRead more
We are given:
sinθ = x and secθ = y.
Step 1: Recall the trigonometric identities
1. The definition of secθ is:
secθ = 1/cosθ.
Therefore, cosθ = 1/secθ = 1/y.
2. The definition of tanθ is:
tanθ = sinθ / cosθ.
Step 2: Substitute the values of sinθ and cosθ
From the problem, sinθ = x and cosθ = 1/y. Substituting these into the formula for tanθ:
tanθ = sinθ / cosθ
= x / (1/y)
Step 3: Simplify the expression
Dividing by 1/y is equivalent to multiplying by y:
tanθ = x * y
= xy
Step 4: Final Answer
Thus, tanθ is equal to xy.
The correct answer is:
a) xy
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/
If 5 tanθ – 4 =0, then the value of 5 sin θ – 4 cos θ/5 sinθ + 4 cos θ is
We are given the equation: 5 tanθ - 4 = 0. Step 1: Solve for tanθ Rearrange the equation to solve for tanθ: 5 tanθ = 4 tanθ = 4/5. Step 2: Express sinθ and cosθ in terms of tanθ Using the identity tanθ = sinθ / cosθ, we can write: sinθ = 4k and cosθ = 5k, where k is a positive constant such that sinRead more
We are given the equation:
5 tanθ – 4 = 0.
Step 1: Solve for tanθ
Rearrange the equation to solve for tanθ:
5 tanθ = 4
tanθ = 4/5.
Step 2: Express sinθ and cosθ in terms of tanθ
Using the identity tanθ = sinθ / cosθ, we can write:
sinθ = 4k and cosθ = 5k,
where k is a positive constant such that sin²θ + cos²θ = 1 (Pythagorean identity).
Substitute sinθ = 4k and cosθ = 5k into the identity:
(4k)² + (5k)² = 1
16k² + 25k² = 1
41k² = 1
k² = 1/41
k = √(1/41).
Thus:
sinθ = 4k = 4/√41,
cosθ = 5k = 5/√41.
Step 3: Simplify the given expression
We are tasked with finding the value of:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ).
Substitute sinθ = 4/√41 and cosθ = 5/√41 into the expression:
Numerator:
5 sinθ – 4 cosθ = 5(4/√41) – 4(5/√41)
= (20/√41) – (20/√41)
= 0.
Denominator:
5 sinθ + 4 cosθ = 5(4/√41) + 4(5/√41)
= (20/√41) + (20/√41)
= 40/√41.
Thus, the entire expression becomes:
(5 sinθ – 4 cosθ) / (5 sinθ + 4 cosθ) = 0 / (40/√41) = 0.
Step 4: Final Answer
The value of the given expression is 0.
The correct answer is:
c) zero
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/
How many linear equation in x and y can be satisfied by x = 1 and y = 2?
To determine how many linear equations in x and y can be satisfied by x=1 and y=2, let's analyze the situation. A linear equation in x and y typically has the form: Ax+By=C where A, B and C are constants. For a given pair ( x = 1, y= 2), we can substitute these values into the equation to see if itRead more
To determine how many linear equations in x and y can be satisfied by x=1 and y=2, let’s analyze the situation.
A linear equation in x and y typically has the form: Ax+By=C
where A, B and C are constants. For a given pair ( x = 1, y= 2), we can substitute these values into the equation to see if it holds.
Step 1: Substitute x=1 and y=2 into the general form of the equation Ax + By = C:
A(1) + B(2) = C
A + 2B = C
This equation can be true from many different values of A, B and C. So, there is not just one equation, but many possible equations that can be formed depending on the values of A and B.
Step 2: General conclusion
There is no unique solution for the values of A, B and C. This means infinitely many linear equations can be satisfied by the point (x=1,y=2).
Conclusion:
The correct answer is (c) infinitely many.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
A linear equation in two variables has
A linear equation in two variables has infinitely many solutions, provided that the equation represents a line in a two-dimensional plane. A linear equation in two variables typically has the form: ax + by = c where a, b, and c are constants. This equation represents a straight line on a coordinateRead more
A linear equation in two variables has infinitely many solutions, provided that the equation represents a line in a two-dimensional plane.
A linear equation in two variables typically has the form: ax + by = c
where a, b, and c are constants. This equation represents a straight line on a coordinate plane, and every point on this line is a solution to the equation.
Infinitely many solutions: Since a straight line has infinitely many points, the equation has infinitely many solutions, as each point on the line represents a valid pair of values for x and y.
Conclusion:
The correct answer is (d) infinitely many solutions.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
The solution of a linear equation in two variables is
The solution of a linear equation in two variables is an ordered pair (x,y) that satisfies the equation when the values of x and y are substituted into the equation. Explanation: A linear equation in two variables typically has the form ax+by=c, where a, b, and c are constants, and x and y are the vRead more
The solution of a linear equation in two variables is an ordered pair (x,y) that satisfies the equation when the values of x and y are substituted into the equation.
Explanation:
A linear equation in two variables typically has the form ax+by=c, where a, b, and c are constants, and x and y are the variables. The solution is the set of values x and y (an ordered pair) that, when substituted into the equation, make the equation true.
Option (a): a number which satisfies the given equation
This is not correct because the solution is not just a single number but an ordered pair of numbers. So, (a) is incorrect.
Option (b): an ordered pair which satisfies the given equation
This is partially correct, but it’s a bit incomplete because it doesn’t clarify that the ordered pair is specific to the equation and needs to satisfy the equation. (b) is incomplete.
Option (c): an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it
This is the most accurate description. The solution is indeed an ordered pair, and when the values of x and y are substituted into the equation, the equation must be satisfied. (c) is correct.
Option (d): none of these
Since option (c) is correct, this option is incorrect. (d) is incorrect.
Conclusion: The correct answer is (c) an ordered pair, whose respective values when substituted for x and y in the given equation, satisfies it.
This question related to Chapter 4 Mathematics Class 9th NCERT. From the Chapter 4 Linear Equation in Two Variables. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/