Question

Sin(x+22)°=cos(2x−7)°

Answer 1

To answer this, it must be noted that the trigonometric functions sine and cosine will have the same values if the angles are complementary (meaning, their sum is 90°). 
                                         90 = (x + 22) + (2x - 7)
The value of x from the equation is 25. 

Answer 2

Answer:

x = 25

Step-by-step explanation:

Given : $\sin (x+22)^{\circ}=\cos (2x-7)^{\circ}$

We have to find the value of x.

Consider the given  $\sin (x+22)^{\circ}=\cos (2x-7)^{\circ}$

We know,

$\sin\theta=\cos(90^{\circ}-\theta)$

Consider the left side  $\sin (x+22)^{\circ}=\cos(90^{\circ}-(x+22)^{\circ})$

thus,

$\sin (x+22)^{\circ}=\cos (2x-7)^{\circ}$ becomes,

$\cos(90^{\circ}-(x+22)^{\circ})=\cos (2x-7)^{\circ}$

Simplify for x,

$\cos(68-x)=\cos (2x-7)$

Thus, 68 - x = 2x - 7

Adding x both side , we have

68 = 3x - 7

Adding 7 both side, we have,

75 = 3x

Divide both side by 3, we have,

x = 25

Thus, x = 25