Given: 1. sin(A - B) = 0 ⇒ A - B = 0° ⇒ A = B. 2. 2cos(A + B) - 1 = 0 ⇒ cos(A + B) = 1/2 ⇒ A + B = 60°. Substitute A = B into A + B = 60°: 2A = 60° ⇒ A = 30°. This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to yoRead more
Given:
1. sin(A – B) = 0 ⇒ A – B = 0° ⇒ A = B.
2. 2cos(A + B) – 1 = 0 ⇒ cos(A + B) = 1/2 ⇒ A + B = 60°.
Substitute A = B into A + B = 60°:
2A = 60° ⇒ A = 30°.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
In a right-angled triangle ABC, with C as the right angle: A + B = 90° (since A + B + C = 180° and C = 90°). Thus, cos(A + B) = cos(90°) = 0. This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.Read more
In a right-angled triangle ABC, with C as the right angle:
A + B = 90° (since A + B + C = 180° and C = 90°).
Thus, cos(A + B) = cos(90°) = 0.
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: cos A + cos²A = 1. We need to find the value of sin²A + sin⁴A. Step 1: Express cos²A in terms of cos A Rearrange the given equation: cos²A = 1 - cos A. Step 2: Use the Pythagorean identity From the Pythagorean identity, we know: sin²A + cos²A = 1. Substitute cos²A = 1 - coRead more
We are given the equation:
cos A + cos²A = 1.
We need to find the value of sin²A + sin⁴A.
Step 1: Express cos²A in terms of cos A
Rearrange the given equation:
cos²A = 1 – cos A.
Step 2: Use the Pythagorean identity
From the Pythagorean identity, we know:
sin²A + cos²A = 1.
Substitute cos²A = 1 – cos A into the identity:
sin²A + (1 – cos A) = 1.
Simplify:
sin²A = cos A.
Step 3: Express sin⁴A in terms of sin²A
Since sin²A = cos A, we can write:
sin⁴A = (sin²A)² = (cos A)² = cos²A.
Step 4: Substitute into sin²A + sin⁴A
Now substitute sin²A = cos A and sin⁴A = cos²A into the expression sin²A + sin⁴A:
sin²A + sin⁴A = cos A + cos²A.
From the given equation, we know:
cos A + cos²A = 1.
Thus:
sin²A + sin⁴A = 1.
This question is from Chapter 8 of the Class 10th NCERT Mathematics book, which deals with the Introduction to Trigonometry. Answer the question according to your understanding of the chapter.
We are given the equations: a cosθ + b sinθ = m — (1) a sinθ - b cosθ = n — (2) We need to find the value of a² + b². Step 1: Square both equations Square both sides of equation (1): (a cosθ + b sinθ)² = m² Expand the left-hand side: a²cos²θ + 2ab cosθ sinθ + b²sin²θ = m² — (3) Square both sides ofRead more
We are given the equations:
a cosθ + b sinθ = m — (1)
a sinθ – b cosθ = n — (2)
We need to find the value of a² + b².
Step 1: Square both equations
Square both sides of equation (1):
(a cosθ + b sinθ)² = m²
Expand the left-hand side:
a²cos²θ + 2ab cosθ sinθ + b²sin²θ = m² — (3)
Square both sides of equation (2):
(a sinθ – b cosθ)² = n²
Expand the left-hand side:
a²sin²θ – 2ab sinθ cosθ + b²cos²θ = n² — (4)
Step 2: Add equations (3) and (4)
Add the expanded forms of equations (3) and (4):
(a²cos²θ + 2ab cosθ sinθ + b²sin²θ) + (a²sin²θ – 2ab sinθ cosθ + b²cos²θ) = m² + n²
Simplify the terms:
– The terms involving 2ab cosθ sinθ cancel out.
– Combine the remaining terms:
a²(cos²θ + sin²θ) + b²(sin²θ + cos²θ) = m² + n²
Step 3: Use the Pythagorean identity
From the Pythagorean identity, we know:
cos²θ + sin²θ = 1.
Substitute this into the equation:
a²(1) + b²(1) = m² + n²
Simplify:
a² + b² = m² + n².
The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled “Introduction to Trigonometry.” Provide your response in line with the concepts covered in this chapter.
We are given the equation: x tan 45° cos 60° = sin 60° cot 60°. Step 1: Substitute the trigonometric values Using standard trigonometric values: - tan 45° = 1, - cos 60° = 1/2, - sin 60° = √3/2, - cot 60° = 1/√3. Substitute these values into the equation: x (1) (1/2) = (√3/2) (1/√3). Step 2: SimplifRead more
We are given the equation:
x tan 45° cos 60° = sin 60° cot 60°.
Step 1: Substitute the trigonometric values
Using standard trigonometric values:
– tan 45° = 1,
– cos 60° = 1/2,
– sin 60° = √3/2,
– cot 60° = 1/√3.
Substitute these values into the equation:
x (1) (1/2) = (√3/2) (1/√3).
Step 2: Simplify both sides
Simplify the left-hand side:
x (1/2) = x/2.
Step 3: Solve for x
Multiply through by 2 to isolate x:
x = 1.
Step 4: Final Answer
The value of x is 1.
The correct answer is:
a) 1
This question pertains to Chapter 8 of the Class 10th NCERT Mathematics textbook, which introduces the topic of Trigonometry. Provide the answer based on your understanding of the chapter.
If A and B are acute angles such that sin (A – B) = 0 and 2cos(A + B) – 1 = 0, thenA =
Given: 1. sin(A - B) = 0 ⇒ A - B = 0° ⇒ A = B. 2. 2cos(A + B) - 1 = 0 ⇒ cos(A + B) = 1/2 ⇒ A + B = 60°. Substitute A = B into A + B = 60°: 2A = 60° ⇒ A = 30°. This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to yoRead more
Given:
1. sin(A – B) = 0 ⇒ A – B = 0° ⇒ A = B.
2. 2cos(A + B) – 1 = 0 ⇒ cos(A + B) = 1/2 ⇒ A + B = 60°.
Substitute A = B into A + B = 60°:
2A = 60° ⇒ A = 30°.
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/
If triangle ABC is right angled at C, then the value of cos (A + B) is
In a right-angled triangle ABC, with C as the right angle: A + B = 90° (since A + B + C = 180° and C = 90°). Thus, cos(A + B) = cos(90°) = 0. This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.Read more
In a right-angled triangle ABC, with C as the right angle:
A + B = 90° (since A + B + C = 180° and C = 90°).
Thus, cos(A + B) = cos(90°) = 0.
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/
If cos A + cos²A = 1, then sin² A + sin⁴ A =
We are given the equation: cos A + cos²A = 1. We need to find the value of sin²A + sin⁴A. Step 1: Express cos²A in terms of cos A Rearrange the given equation: cos²A = 1 - cos A. Step 2: Use the Pythagorean identity From the Pythagorean identity, we know: sin²A + cos²A = 1. Substitute cos²A = 1 - coRead more
We are given the equation:
cos A + cos²A = 1.
We need to find the value of sin²A + sin⁴A.
Step 1: Express cos²A in terms of cos A
Rearrange the given equation:
cos²A = 1 – cos A.
Step 2: Use the Pythagorean identity
From the Pythagorean identity, we know:
sin²A + cos²A = 1.
Substitute cos²A = 1 – cos A into the identity:
sin²A + (1 – cos A) = 1.
Simplify:
sin²A = cos A.
Step 3: Express sin⁴A in terms of sin²A
Since sin²A = cos A, we can write:
sin⁴A = (sin²A)² = (cos A)² = cos²A.
Step 4: Substitute into sin²A + sin⁴A
Now substitute sin²A = cos A and sin⁴A = cos²A into the expression sin²A + sin⁴A:
sin²A + sin⁴A = cos A + cos²A.
From the given equation, we know:
cos A + cos²A = 1.
Thus:
sin²A + sin⁴A = 1.
This question is from Chapter 8 of the Class 10th NCERT Mathematics book, which deals with the Introduction to Trigonometry. Answer the question according to your understanding of the chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If a cos θ + b sin θ = m and a sin θ – b cos θ = n, then a² + b² =
We are given the equations: a cosθ + b sinθ = m — (1) a sinθ - b cosθ = n — (2) We need to find the value of a² + b². Step 1: Square both equations Square both sides of equation (1): (a cosθ + b sinθ)² = m² Expand the left-hand side: a²cos²θ + 2ab cosθ sinθ + b²sin²θ = m² — (3) Square both sides ofRead more
We are given the equations:
a cosθ + b sinθ = m — (1)
a sinθ – b cosθ = n — (2)
We need to find the value of a² + b².
Step 1: Square both equations
Square both sides of equation (1):
(a cosθ + b sinθ)² = m²
Expand the left-hand side:
a²cos²θ + 2ab cosθ sinθ + b²sin²θ = m² — (3)
Square both sides of equation (2):
(a sinθ – b cosθ)² = n²
Expand the left-hand side:
a²sin²θ – 2ab sinθ cosθ + b²cos²θ = n² — (4)
Step 2: Add equations (3) and (4)
Add the expanded forms of equations (3) and (4):
(a²cos²θ + 2ab cosθ sinθ + b²sin²θ) + (a²sin²θ – 2ab sinθ cosθ + b²cos²θ) = m² + n²
Simplify the terms:
– The terms involving 2ab cosθ sinθ cancel out.
– Combine the remaining terms:
a²(cos²θ + sin²θ) + b²(sin²θ + cos²θ) = m² + n²
Step 3: Use the Pythagorean identity
From the Pythagorean identity, we know:
cos²θ + sin²θ = 1.
Substitute this into the equation:
a²(1) + b²(1) = m² + n²
Simplify:
a² + b² = m² + n².
The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled “Introduction to Trigonometry.” Provide your response in line with the concepts covered in this chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions/class-10/maths/
If x tan 45° cos 60° = sin 60° cot 60°, then x is equal to
We are given the equation: x tan 45° cos 60° = sin 60° cot 60°. Step 1: Substitute the trigonometric values Using standard trigonometric values: - tan 45° = 1, - cos 60° = 1/2, - sin 60° = √3/2, - cot 60° = 1/√3. Substitute these values into the equation: x (1) (1/2) = (√3/2) (1/√3). Step 2: SimplifRead more
We are given the equation:
x tan 45° cos 60° = sin 60° cot 60°.
Step 1: Substitute the trigonometric values
Using standard trigonometric values:
– tan 45° = 1,
– cos 60° = 1/2,
– sin 60° = √3/2,
– cot 60° = 1/√3.
Substitute these values into the equation:
x (1) (1/2) = (√3/2) (1/√3).
Step 2: Simplify both sides
Simplify the left-hand side:
x (1/2) = x/2.
Simplify the right-hand side:
(√3/2) (1/√3) = (√3 / √3) / 2 = 1/2.
Thus, the equation becomes:
x/2 = 1/2.
Step 3: Solve for x
Multiply through by 2 to isolate x:
x = 1.
Step 4: Final Answer
The value of x is 1.
The correct answer is:
a) 1
This question pertains to Chapter 8 of the Class 10th NCERT Mathematics textbook, which introduces the topic of Trigonometry. Provide the answer based on your understanding of the chapter.
For more please visit here:
See lesshttps://www.tiwariacademy.in/ncert-solutions-class-10-maths-chapter-8/