Question

If cos x = sin(20 + x)° and 0° < x < 90°, the value of x is

Answer 1

Answer:

x=35

Step-by-step explanation:

Answer 2

ANSWER

x=35°

EXPLANATION

We want to find the value of x, when

$\cos(x) = \sin(20 + x) \degree$

and 0°<x<90°

Recall that the sine and cosine are complementary trigonometric ratios.

Hence cos x = sin (90-x)

Our equation now, becomes;

$\sin(90 - x) \degree= \sin(20 + x) \degree$

We now equate the argument to get,

$90 - x=20 + x$

Group similar terms to obtain:

$90 - 20 = x + x$

$70 = 2x$

This implies that,

$x = 35 \degree$