If sin 3A = cos (A - 26°), then find the value of A, where 3A is an acute angle.

Question

Accepted Answer

Given: sin 3A = cos (A - 26°)

We know that sin θ = cos (90° - θ).

So, sin 3A = cos (A - 26°) implies:
3A = 90° - (A - 26°) or 3A = 90° + (A - 26°) (since cos x = cos y implies x = y or x = 360° - y, but here angles are acute so consider principal values)

Case 1:
3A = 90° - A + 26°
3A = 116° - A
3A + A = 116°
4A = 116°
A = 29°

Check if 3A is acute:
3 × 29° = 87°, which is acute.

Case 2:
3A = 90° + A - 26°
3A = 64° + A
3A - A = 64°
2A = 64°
A = 32°

Check if 3A is acute:
3 × 32° = 96°, which is not acute.

Therefore, the valid solution is A = 29°.

Answer

Answer

Answer