Question

3cosx+2cos^2(3п/2-x)=0

Answer 1

$3cosx+2cos^2( frac{3 pi }{2} -x)=0$

$3cosx+2sin^2(x)=0$

$3cosx+2(1-cos^2x)=0$

$3cosx+2-2cos^2x=0 \ \ 2cos^2x-3cosx-2=0$

cosx=t ; t∈[-1;1]

$2t^2-3t-2=0 ; t = -frac{1}{2} ; 2$

t=2∉[-1;1], значит, t=-1/2

$cosx=- frac{1}{2}$

x=+/- 2π/3+2πk, k∈Z