Question

Calculați sin x radical din 1 - cos la 2 x - cos x radical 1 - sin la 2 x , x e (pi/2 , pi)

Answer 1

[tex]\sin x \sqrt{1-\cos^2x}-\cos x\sqrt{1-\sin^2 x}=\\ \sin x\cdot \sin^2x -\cos x\cdot \cos^2 x=\\ \sin^3 x-\cos^3x=\\ (\sin x-\cos x)(\sin^2 x+\sin x\cdot \cos x+\cos^2 x)=\\ (\sin x-\cos x)(1+\sin x\cdot \cos x)[/tex]