Question

What is the value of x?

sin(x+37)°=cos(2x+8)°

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x =

Answer 1

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°

Answer 2

In the trigonometry sin and cosine are the complementary angle. The value of the x is 15 units.

Given information-

The given trigonometric equation in the problem is,

$\sin(x+37)^o=\cos(2x+8)^o$

Complementary angle

In the trigonometry sin and cosine are the complementary angle. It can be written as,

$\sin\theta=\cos(90-\theta)$

Use the above formula to solve the given equation,

$\begin{aligned}\\ \sin(x+37)^o&=\cos(2x+8)^o\\ \cos[90-(x+37)]^o&=\cos(2x+8)^o\\\\ \cos(90-x-37)^o&=\cos(2x+8)^o\\\\ \cos(53-x)^o&=\cos(2x+8)^o\\ \end$

Compare the two cosine function using the property of cosine function,

$\begin{aligned}\\ 53-x&=2x+8\\ 2x+x&=53-8\\ 3x&=45\\ x&=\dfrac{45}{3}\\ x&=15\\ \end$

Thus the value of the x is 15 units.

Learn more about the complementary angles here;

https://brainly.com/question/2882938