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

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Question 1077075: If sin 3A=cos(A-26°) where 3A is an acute angle,find the value of A.
Answer by ikleyn(52779) About Me  (Show Source):
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If sin 3A=cos(A-26°) where 3A is an acute angle,find the value of A.
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Use the identity cos%28x%29 = sin%28pi%2F2-x%29, which is the same as cos(x) = sin(90°-x).

It gives

sin(3A) = sin(90° - A + 26°).


The last equation implies (since all the angles are in QI)

3A = 90° - A + 26°,   or

4A = 116°,

A = 116%2F4 = 29°.


Answer.  A = 29°.

Solved.