If 2 × cos(A + B) = 2 × sin(A - B) = 1, find the value of A and B.1.

1.	If 2 × cos(A + B) = 2 × sin(A - B) = 1, find the value of A and B.1. A = 45° and B = 15° 2. A = 90° and B = 0° 3. A = 30° and B = 60° 4. A = 15° and B = 45°
Answer» Correct Answer - Option 1 : A = 45° and B = 15° Given 2 × cos(A + B) = 2 × sin(A - B) = 1 Concept Here all three identities are equal to each other so, take first any two identities then the other two identities. Calculation Let 2 × cos(A + B) = 1 ⇒ cos(A + B) = (1/2) ⇒ cos(A + B) = cos 60° ⇒ A + B = 60° ....(1) Now, Let 2 × sin(A - B) = 1 ⇒ sin(A - B) = (1/2) ⇒ sin(A - B) = sin30° ⇒ A - B = 30° ....(2) Now, add equation (1) and (2) ⇒ (A + B) + (A - B) = 60° + 30° ⇒ 2A = 90° ⇒ A = (90°/2) ⇒ A = 45° Now put the value of A in equation (1) ⇒ 45° + B = 60° ⇒ B = 60° - 45° ⇒ B = 15° ∴ A = 45° and B = 15°

If 2 × cos(A + B) = 2 × sin(A - B) = 1, find the value of A and B.1. A = 45° and B = 15° 2. A = 90° and B = 0° 3. A = 30° and B = 60° 4. A = 15° and B = 45°

Answer» Correct Answer - Option 1 : A = 45° and B = 15°

Given

2 × cos(A + B) = 2 × sin(A - B) = 1

Concept

Here all three identities are equal to each other so, take first any two identities then the other two identities.

Calculation

Let 2 × cos(A + B) = 1

⇒ cos(A + B) = (1/2)

⇒ cos(A + B) = cos 60°

⇒ A + B = 60° ....(1)

Now,

Let 2 × sin(A - B) = 1

⇒ sin(A - B) = (1/2)

⇒ sin(A - B) = sin30°

⇒ A - B = 30° ....(2)

Now, add equation (1) and (2)

⇒ (A + B) + (A - B) = 60° + 30°

⇒ 2A = 90°

⇒ A = (90°/2)

⇒ A = 45°

Now put the value of A in equation (1)

⇒ 45° + B = 60°

⇒ B = 60° - 45°

⇒ B = 15°

∴ A = 45° and B = 15°