What is the value of x?sin(x+37)°=cos(2x+8)°Enter your answer in the box.x =

Applying the trig formula: sin a = cos (90 - a)
cos (2x + 8) = sin (x + 37) = cos (90 - x - 37) = cos (53 - x)
Property of the cosine function -->
(
2
x
+
8
)
=
±
(
53
−
x
)

a. 2x + 8 = 53 - x
3x = 45
x
=
15
∘

b. 2x + 8 = - 53 + x
x
=
−
61
∘

For general answers, add
k
360
∘

Check by calculator.
x = 15 --> sin (x + 37) = sin 52 = 0.788
cos (2x + 8) = cos (38) = 0.788. Proved
x = - 61 --> sin (x + 37) = sin (- 24) = - sin 24 = - 0.407
cos (2x + 8) = cos (-122 + 8) = cos (- 114) = - 0.407. Proved