Question

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

Answer 1

SOLUTION :  

Given : sin 3A = cos(A - 26°), 3A is an acute angle.

sin 3A = sin(90° - (A - 26°))

sin 3A = sin(90° - A + 26°)

sin 3A = sin(90°  + 26° - A)

sin 3A = sin(116° - A)

3A = 116° - A

3A + A = 116°

4A = 116∘

A = 116°/4

A = 29°

Hence,  the value of A is 29°  

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Answer 2

Given sin 3A=cos(A − 26) 
⇒ cos(90 − 3A) = cos(A − 26)
⇒ (90 − 3A) = (A − 26) 
⇒ 4A = 116°
 ∴ A = 29°