Question

5sinx-cos^2x+2sin^2x=1​

Answer 1

$5sin(x)-cos^2(x)+2sin^2(x)=1\\5sin(x)-1+sin^2(x)+2sin^2(x)-1=0\\3sin^2(x)+5sin(x)-2=0\\D_{sin(x)}=25+24=49\\sin(x)=-2\\sin(x)=\frac{1}{3}<=>x=(-1)^karcsin(\frac{1}{3} )+\pi k$

k∈Z