Question

Sin(x+22)°=cos(2x−7)°

Answer 1

x = 25

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

Answer 2

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.