Question

find the x-values that are solutions of the equation

5cot^2x-15=0

Answer 1

rearrange a little bit to make this easier \[5\cot^2 x=15 \rightarrow \cot^2 x = 3 \rightarrow \cos^2 x = 3\sin^2x\rightarrow \cos x = \sqrt{3} \sin x\] from here you're on your own

Answer 2

where did the sine come out of?
i understand up to cot^2x=3

Answer 3

\[cot(x) = \frac{1}{tan(x)}~\text{and}~~ tan(x)=\frac{sin(x)}{cos(x)}\]