Question

If sin(A – B) = 0, where 0° ≤ A, B ≥ 90° then find the value of 2 sin A × sin B + 2 cos A × cos B 

1. Even prime number less than 5
2. 2
3. 1
4. Both options 1 and 2 are correct
5. 3

Answer 1

Correct Answer - Option 4 : Both options 1 and 2 are correct

Given:

Value of sin(A – B) = 0

Identity used:

sin² A + cos² A = 1

Calculation:

As, sin(A – B ) = 0

⇒ sin(A – B ) = sin 0° 

⇒ A – B = 0

⇒ A = B

We have to find the value of 2 sin A × sin B + 2 cos A × cos B 

⇒ 2 sin A × sin B + 2 cos A × cos B 

⇒ 2 × (sin A × sin A + cos A × cos A)

⇒  2 × (sin² A + cos² A)

⇒ 2

Now 2 is also the even prime number less than 5.

∴ Both options 1 and 2 are correct.