Question

2 cos*2 x-3sin x -3=0

Answer 1

$2cos^{2} x-3sinx-3=0 \ 2(1-sin ^{2} x)-3sinx-3=0 \ 2-2sin^{2} x-3sinx-3=0 \ -2sin^{2} x-3sinx-1=0/*(-1)\2sin^{2} x+3sinx+1=0 \ sinx=t \ 2t^{2} +3t+1=0 \ D=9-8=1 \ sqrt{D} =1 \ t _{1} = frac{-3+1}{4} = frac{-2}{4} =- frac{1}{2} \ t _{2} = frac{-3-1}{4} =- frac{4}{4} =-1 \ sinx=- frac{1}{2} \ x=(-1) ^{n+1} frac{ pi }{6} + pi n$

$sinx=-1 \ x=- frac{ pi }{2} +2 pi m$

n∈Z
m∈Z