Question

Find all solutions to the equation. 7 sin2x - 14 sin x + 2 = -5

Answer 1

\(\Large 7sin^2x-14sinx+2=-5\\\Large 7sin^2x-14sinx+7=0\\\Large sin^2x-2sinx+1=0\)

Let \(\Large t=sinx\)

the equation become:
\(\Large t^2-2t+1=0\\\Large \Rightarrow t=1\)
Thus, \(\Large sinx=1 \Rightarrow x=\frac{\pi}{2}+2k\pi\ \ (k\in Z) \)