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  1. Asked: In:

    If a cos θ + b sinθ = 4 and a sin θ – b cos θ = 3, then a² + b² =

    Moksh Dixit

    We are given the equations: a cosθ + b sinθ = 4 — (1) a sinθ - b cosθ = 3 — (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 = 4² Expand the left-hand side: a² cos²θ + 2ab cosθ sinθ + b² sin²θ = 16 — (3) Square both sides oRead more

    We are given the equations:
    a cosθ + b sinθ = 4 — (1)
    a sinθ – b cosθ = 3 — (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 = 4²
    Expand the left-hand side:
    a² cos²θ + 2ab cosθ sinθ + b² sin²θ = 16 — (3)

    Square both sides of equation (2):
    (a sinθ – b cosθ)² = 3²
    Expand the left-hand side:
    a² sin²θ – 2ab sinθ cosθ + b² cos²θ = 9 — (4)

    Step 2: Add equations (3) and (4)
    Add the expanded forms of equations (3) and (4):
    (a² cos²θ + 2ab cosθ sinθ + b² sin²θ) + (a² sin²θ – 2ab sinθ cosθ + b² cos²θ) = 16 + 9

    Simplify the terms:
    – The terms involving 2ab cosθ sinθ cancel out.
    – Combine the remaining terms:
    a² (cos²θ + sin²θ) + b² (sin²θ + cos²θ) = 25

    Step 3: Use the Pythagorean identity
    From the Pythagorean identity, we know:
    cos²θ + sin²θ = 1.

    Substitute this into the equation:
    a² (1) + b² (1) = 25

    Simplify:
    a² + b² = 25.
    The question is connected to Chapter 8, “Introduction to Trigonometry,” in the Class 10th NCERT Mathematics book. Respond based on your comprehension of the chapter.

    For more please visit here:
    https://www.tiwariacademy.in/ncert-solutions/class-10/maths/

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    • 38
  2. Asked: In:

    If sin θ – cos θ = 0, then the value of sin⁴ θ + cos⁴ θ is

    Moksh Dixit

    Given: sinθ - cosθ = 0. 1. Solve for θ: sinθ = cosθ ⇒ tanθ = 1 ⇒ θ = 45°. 2. For θ = 45°: sinθ = cosθ = 1/√2. 3. Calculate sin⁴θ + cos⁴θ: sin⁴θ + cos⁴θ = (sin²θ)² + (cos²θ)² = (1/2)² + (1/2)² = 1/4 + 1/4 = 1/2. The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled "Read more

    Given: sinθ – cosθ = 0.

    1. Solve for θ:
    sinθ = cosθ ⇒ tanθ = 1 ⇒ θ = 45°.

    2. For θ = 45°:
    sinθ = cosθ = 1/√2.

    3. Calculate sin⁴θ + cos⁴θ:
    sin⁴θ + cos⁴θ = (sin²θ)² + (cos²θ)²
    = (1/2)² + (1/2)²
    = 1/4 + 1/4
    = 1/2.
    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:
    https://www.tiwariacademy.in/ncert-solutions/class-10/maths/

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    • 26
  3. Asked: In:

    The value of (1 + cot θ – cosec θ) (1 + tan θ + sec θ) is

    Moksh Dixit

    Given: (1 + cotθ - cosecθ)(1 + tanθ + secθ). 1. Rewrite in terms of sinθ and cosθ: (1 + cosθ/sinθ - 1/sinθ)(1 + sinθ/cosθ + 1/cosθ). 2. Simplify each factor: First factor: (sinθ + cosθ - 1)/sinθ. Second factor: (cosθ + sinθ + 1)/cosθ. 3. Multiply and simplify: Numerator: (sinθ + cosθ)² - 1 = 2sinθcoRead more

    Given: (1 + cotθ – cosecθ)(1 + tanθ + secθ).

    1. Rewrite in terms of sinθ and cosθ:
    (1 + cosθ/sinθ – 1/sinθ)(1 + sinθ/cosθ + 1/cosθ).

    2. Simplify each factor:
    First factor: (sinθ + cosθ – 1)/sinθ.
    Second factor: (cosθ + sinθ + 1)/cosθ.

    3. Multiply and simplify:
    Numerator: (sinθ + cosθ)² – 1 = 2sinθcosθ.
    Denominator: sinθcosθ.

    4. Result: 2sinθcosθ / sinθcosθ = 2.
    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:
    https://www.tiwariacademy.in/ncert-solutions/class-10/maths/

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    • 21
  5. Asked: In:

    If A and B are acute angles such that sin (A – B) = 0 and 2cos(A + B) – 1 = 0, thenA =

    Best Answer
    Moksh Dixit

    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:
    https://www.tiwariacademy.in/ncert-solutions/class-10/maths/

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    • 40
  6. Asked: In:

    If triangle ABC is right angled at C, then the value of cos (A + B) is

    Best Answer
    Moksh Dixit

    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:
    https://www.tiwariacademy.in/ncert-solutions/class-10/maths/

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    • 25
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