We are given the following equation:
[tex]sinxcosx=\frac{1}{4}[/tex]
First, we will multiply both sides by 2:
[tex]2sinxcosx=\frac{2}{4}[/tex]
Simplifying the right side:
[tex]2sinxcosx=\frac{1}{2}[/tex]
Now, we use the following trigonometric identity:
[tex]2sinxcosx=sin(2x)[/tex]
Applying the property we get:
[tex]sin(2x)=\frac{1}{2}[/tex][tex]sin(2x)=\frac{1}{2}[/tex]
Now, we take the inverse function of sine:
[tex]2x=arcsin(\frac{1}{2})[/tex]
Solving the operation on the right side we have two possible solutions:
[tex]2x=\frac{\pi}{6}+2n\pi[/tex]
and:
[tex]2x=\frac{5\pi}{6}+2n\pi[/tex]
Dividing both sides by 2:
[tex]x=\frac{\pi}{12}+n\pi[/tex]
and
[tex]x=\frac{5\pi}{12}+n\pi[/tex]
