Question

Решить уравнение2sinx-2sin^2 x=cos^2 x

Answer 1

$2sinx-2sin ^{2} x=cos ^{2} x \\ 2sinx-2sin ^{2} x-cos ^{2}x=0 \\ 2sinx-2sin ^{2} x- (1-sin ^{2} x) =0 \\ 2 sinx-2sin ^{2} x- 1+sin ^{2} x=0 \\ 2sinx-sin ^{2} x-1=0 \\ sinx=t \\ 2t-t ^{2} -1=0 \\ D=8 \\ \sqrt{D} =2 \sqrt{2} \\ t_{1}= 1+ \sqrt{2} \\ t_{2} =1- \sqrt{2} \\ cosx \neq 1+ \sqrt{2} \\ cosx=1- \sqrt{2} \\ x=+-(arccos(1- \sqrt{2} ))+2 \pi n$