Question

найти cos4x, если cosx+sinx=0,5

Answer 1

$cos x+sin x=0.5;\ (cos x+sin x)^2=0.5^2;\ cos^2 x+2sin x cos x+sin^2 x=0.25;\ 1+sin (2x)=0.25;\ sin (2x)=-0.75;\ sin^2 (2x)=(-0.75)^2=0.5625;\ cos^2 (2x)=1-sin^2 (2x)=1-0.5625=0.4375;\ cos (4x)=2cos^2 (2x)-1=2*0.4375-1=1.75$