Question

Find the value of A if sin 2A = cos (A – 6°) where 2A and (A – 6°) are acute angles.

Answer 1

Given: sin 2A = cos(A – 6°) and 2A and (A – 6°) are acute angles.

Step-wise calculation:

1. Use cos x = sin (90° – x): 

cos (A – 6°) = sin (90° – (A – 6°)) 

= sin (96° – A)

2. So, sin 2A = sin (96° – A). 

For acute angles, the principal possibility is equality of angles:

2A = 96° – A

3. Solve: 3A = 96°

⇒ A = 32°

4. Check the acute-angle conditions:

2A = 64° and A – 6° = 26°, both acute so A = 32° is valid.