Answer:
[tex]\bold{x = 34^\circ}[/tex]
Step-by-step explanation:
Given:
[tex]cos x = sin (x + 22^\circ)[/tex]
To solve:
The given equation.
Solution:
First of all, let us consider an important property of sine and cosine.
[tex]sin(90^\circ-\theta )=cos\theta[/tex]
OR
[tex]cos(90^\circ-\theta )=sin\theta[/tex]
We can apply above property to solve for [tex]x[/tex] as per given equation.
[tex]cos x = sin (x + 22^\circ)[/tex]
Changing [tex]cosx[/tex] to sine form:
[tex]cosx=sin(90^\circ-x)[/tex]
[tex]cosx=sin(90^\circ-x) = sin(x+22^\circ)[/tex]
[tex]\therefore 90^\circ-x=x+22^\circ\\\Rightarrow 90^\circ-22^\circ=x+x\\\Rightarrow 2x=68^\circ\\\Rightarrow \bold{x = 34^\circ}[/tex]
So, solution to the equation [tex]cos x = sin (x + 22^\circ)[/tex] is:
[tex]\bold{x = 34^\circ}[/tex]
