What is the value of x?

sin (x+37) °=cos (2x+8) °

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x =

Using trigonometry formula: sin a = cos (90 - a)

cos (2x + 8) = sin (x + 37)

cos (90 - x - 37) = cos (53 - x)

Property of cosine function: (2x + 8) = ± (53 - x)

2x + 8 = 53 - x

3x = 45

x = 15°

2x + 8 = - 53 + x

x = - 61°

Answer: x = 15°, x = - 61°