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

If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees

Solution:

Given that:

We know that,

Taking cos x as common,

By trignometric functions,

sin 20 = 0.34202

cos 20 = 0.939692

So,

Therefore,

x = arc tan (0.7002)

x = 35 degrees

Therefore value of x is 35 degrees

cos x = sin (20 + x)

sin and cos are co - functions, which means that:

cos x = cos [90 - (20 + x)]

cos x = cos (90 - 20 - x)

cos x = cos (70 - x)

Therefore, x = 70 - x

x + x = 70

2x = 70

x = 35

Therefore value of x is 35 degrees