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.
The number of zeroes ( or roots) of a polynomial is determined by its degree. The degree of a polynomial is the highest exponent of the variable. Given Polynomial: x³ + x - 3 - 3x² Step 1: Arrange in Standard Form Rearrange the terms in descending order of powers of x: x³ - 3x² + x - 3 Step 2: IdentRead more
The number of zeroes ( or roots) of a polynomial is determined by its degree. The degree of a polynomial is the highest exponent of the variable.
Given Polynomial: x³ + x – 3 – 3x²
Step 1: Arrange in Standard Form
Rearrange the terms in descending order of powers of x:
x³ – 3x² + x – 3
Step 2: Identify the Degree
The highest power of x is 3.
A polynomial of degree n can have at most n zeroes.
Conclusion: Since the given polynomial is of degree 3, it has three zeroes ( real or complex). Thus the correct answer is (d) 3.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. Give answer according to your understanding.
Correct option (a) 2x A polynomial consists of terms where the variable has only non-negative integer exponents. Analyzing Each Option: (a). 2x - The exponent of x is 1, which is a non-negative integer. This is a valid term of a polynomial. (b). 3/x - This can be rewritten as 3x ⁻¹. Since the exponeRead more
Correct option (a) 2x
A polynomial consists of terms where the variable has only non-negative integer exponents.
Analyzing Each Option:
(a). 2x – The exponent of x is 1, which is a non-negative integer. This is a valid term of a polynomial.
(b). 3/x – This can be rewritten as 3x ⁻¹. Since the exponent is negative, this is not a polynomial term.
(c). x√x – We rewrite √x as x¹/², so:
x√x = x.x¹/² = x ³/² Since the exponent 3/2 is not an integer, this is not a polynomial terms.
(d). √x – since √x = x ¹/², and the exponent 1/2 is not a integer, this is not a polynomial term.
Final Answer: The correct answer is (a) 2x.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. Give answer according to your understanding.
We need to find the value of: 104 x 96 Step 1: Use the Difference of Squares Formula We rewrite the numbers as: 104 x 96 = (100 + 4) (100 - 4) Using the identify: (a + b) (a - b) = a² - b² where a = 100 and b = 4: 104 × 96 = 100² - 4² Step 2: Compute the Values 100² = 10000 4² = 16 10000 - 16 = 9984Read more
We need to find the value of: 104 x 96
Step 1: Use the Difference of Squares Formula
We rewrite the numbers as: 104 x 96 = (100 + 4) (100 – 4)
Using the identify: (a + b) (a – b) = a² – b²
where a = 100 and b = 4:
104 × 96 = 100² – 4²
Step 2: Compute the Values
100² = 10000
4² = 16
10000 – 16 = 9984
Final Answer: The correct option is: (a) 9984.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. 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/
The number of zeroes of the polynomial x³ + x – 3 – 3x² is
The number of zeroes ( or roots) of a polynomial is determined by its degree. The degree of a polynomial is the highest exponent of the variable. Given Polynomial: x³ + x - 3 - 3x² Step 1: Arrange in Standard Form Rearrange the terms in descending order of powers of x: x³ - 3x² + x - 3 Step 2: IdentRead more
The number of zeroes ( or roots) of a polynomial is determined by its degree. The degree of a polynomial is the highest exponent of the variable.
Given Polynomial: x³ + x – 3 – 3x²
Step 1: Arrange in Standard Form
Rearrange the terms in descending order of powers of x:
x³ – 3x² + x – 3
Step 2: Identify the Degree
The highest power of x is 3.
A polynomial of degree n can have at most n zeroes.
Conclusion: Since the given polynomial is of degree 3, it has three zeroes ( real or complex). Thus the correct answer is (d) 3.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
Which of the following is a term of a polynomial?
Correct option (a) 2x A polynomial consists of terms where the variable has only non-negative integer exponents. Analyzing Each Option: (a). 2x - The exponent of x is 1, which is a non-negative integer. This is a valid term of a polynomial. (b). 3/x - This can be rewritten as 3x ⁻¹. Since the exponeRead more
Correct option (a) 2x
A polynomial consists of terms where the variable has only non-negative integer exponents.
Analyzing Each Option:
(a). 2x – The exponent of x is 1, which is a non-negative integer. This is a valid term of a polynomial.
(b). 3/x – This can be rewritten as 3x ⁻¹. Since the exponent is negative, this is not a polynomial term.
(c). x√x – We rewrite √x as x¹/², so:
x√x = x.x¹/² = x ³/² Since the exponent 3/2 is not an integer, this is not a polynomial terms.
(d). √x – since √x = x ¹/², and the exponent 1/2 is not a integer, this is not a polynomial term.
Final Answer: The correct answer is (a) 2x.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/
The value of 104 x 96 is:
We need to find the value of: 104 x 96 Step 1: Use the Difference of Squares Formula We rewrite the numbers as: 104 x 96 = (100 + 4) (100 - 4) Using the identify: (a + b) (a - b) = a² - b² where a = 100 and b = 4: 104 × 96 = 100² - 4² Step 2: Compute the Values 100² = 10000 4² = 16 10000 - 16 = 9984Read more
We need to find the value of: 104 x 96
Step 1: Use the Difference of Squares Formula
We rewrite the numbers as: 104 x 96 = (100 + 4) (100 – 4)
Using the identify: (a + b) (a – b) = a² – b²
where a = 100 and b = 4:
104 × 96 = 100² – 4²
Step 2: Compute the Values
100² = 10000
4² = 16
10000 – 16 = 9984
Final Answer: The correct option is: (a) 9984.
This question related to Chapter 2 Mathematics Class 9th NCERT. From the Chapter 2 Polynomials. Give answer according to your understanding.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-9/maths/