sin^2x=1-cos^2x

2^(sin^2x)+2^(1-sin^2x)=3

2sin^2x=t

t+2/t=3

t^2-3t+2=0

D=9-8=1

t1=(3+1)/2=2; 2^sin^2=2; sin^2=1; x=pi/2+pik

t2=(3-1)/2=1; 2sin^2=1; sin^2x=0; x=pik

Ответ x={pik;pi/2+pik}