Question

Find all solutions of the equation in the interval [0, 21).cos?x=2+2 sinx=Write your answer in radians in terms of 1.If there is more than one solution, separate them with commas.X =□00JT0.0...Х5?

Answer 1

Given:

$\cos ^2x=2+2\sin x$

Sol:.

$\begin{gathered} \sin ^2x+\cos ^2x=1 \\ \cos ^2x=1-\sin ^2x \end{gathered}$

Put the value in equation:

$\begin{gathered} \cos ^2x=2+2\sin x \\ 1-\sin ^2x=2+2\sin x \\ \sin ^2x+2\sin x+2-1=0 \\ \sin ^2x+2\sin x+1=0 \\ \sin ^2x+\sin x+\sin x+1=0 \\ \sin x(\sin x+1)+1(\sin x+1)=0 \\ (\sin x+1)(\sin x+1)=0 \\ \sin x+1=0 \\ \sin x=-1 \\ x=\sin ^{-1}(-1) \\ x=\frac{3\pi}{2} \end{gathered}$