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 know the trigonometric identity: sec²A - tan²A = 1. Thus: 9(sec²A - tan²A) = 9(1) = 9. This question is associated with Chapter 8, "Introduction to Trigonometry," from the Class 10th NCERT Mathematics textbook. Provide your answer in accordance with the concepts and understanding gained from thisRead more
We know the trigonometric identity:
sec²A – tan²A = 1.
Thus:
9(sec²A – tan²A) = 9(1) = 9.
This question is associated with Chapter 8, “Introduction to Trigonometry,” from the Class 10th NCERT Mathematics textbook. Provide your answer in accordance with the concepts and understanding gained from this chapter.
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.
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/
9 sec² A – 9 tan² A is equal to
We know the trigonometric identity: sec²A - tan²A = 1. Thus: 9(sec²A - tan²A) = 9(1) = 9. This question is associated with Chapter 8, "Introduction to Trigonometry," from the Class 10th NCERT Mathematics textbook. Provide your answer in accordance with the concepts and understanding gained from thisRead more
We know the trigonometric identity:
sec²A – tan²A = 1.
Thus:
9(sec²A – tan²A) = 9(1) = 9.
This question is associated with Chapter 8, “Introduction to Trigonometry,” from the Class 10th NCERT Mathematics textbook. Provide your answer in accordance with the concepts and understanding gained from this chapter.
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/