If cos x= sin(20 + x)° and 0° < x < 90° then value of x is 35 degrees
Solution:
Given that:
[tex]cos x= sin (20 + x)[/tex]
We know that,
[tex]sin (a+b)=sin a \times cos b+cos a \times sin b[/tex]
[tex]cos x= sin (20 + x) = sin 20 cos x + cos 20 sin x[/tex]
[tex]cos x-sin20 \times cos x=cos 20 \times sin x[/tex]
Taking cos x as common,
[tex]cos x(1-sin 20)=cos 20 \times sin x[/tex]
[tex]\frac{(1-sin 20)}{(cos 20)}=\frac{sin x}{cos x }\\\\tan x = \frac{(1-sin 20)}{(cos 20)}[/tex]
By trignometric functions,
sin 20 = 0.34202
cos 20 = 0.939692
So,
[tex]tan x = \frac{1 - 0.34202}{0.939692}\\\\tan x = 0.7002[/tex]
Therefore,
x = arc tan (0.7002)
x = 35 degrees
Therefore value of x is 35 degrees
Method 2:
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
