SOLUTION: Please help me solve this question If alpha and beta are 2 positive acute angles satisfying alpha - beta = 15 degree and sin alpha = cos 2 beta then find value of alpha + beta

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Question 1036529: Please help me solve this question
If alpha and beta are 2 positive acute angles satisfying alpha - beta = 15 degree and sin alpha = cos 2 beta then find value of alpha + beta
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Please help me solve this question
If alpha and beta are 2 positive acute angles satisfying alpha - beta = 15 degree and sin alpha = cos 2 beta then find value of alpha + beta
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If sin%28alpha%29 = cos%282%2Abeta%29, then

sin%28alpha%29 = sin%28pi%2F2-2%2Abeta%29.

Due to constrains imposed on alpha and beta, it implies that

alpha = pi%2F2+-+2%2Abeta,   or

alpha+%2B+2%2Abeta = pi%2F2.    (1)

From the condition, we also have the second equation 

alpha+-+beta = pi%2F12.      (2)     ( pi%2F12 = 15 degs)

Distract equation (2) from (1) (both sides). You will get

3%2Abeta = pi%2F2+-+pi%2F12 = %285pi%29%2F12.

Hence, beta = %285pi%29%2F36 = %285%2A180%29%2F36 = 5*5 = 25 degs.

Then alpha = pi%2F2+-+2%2Abeta = pi%2F2+-+%2810pi%29%2F36 = %28%2818-10%29%2Api%29%2F36 = %288pi%29%2F36 = 2pi%2F9 = 40 degs.

Answer.  alpha = 2pi%2F9 = 40 degs;  beta = %285pi%29%2F36 = 25 degs.