Question

Anybody know the right answer?

Answer 1

`\text{Use:}\\\\\sin(x-y)=\sin x\cos y-\sin y\cos x\\\\\cos(x-y)=\cos x\cos y+\sin x\sin y`

`\sin\left((\pi)/(2)-x\right)=\sin(\pi)/(2)\cos x-\sin x\cos(\pi)/(2)=1\cos x-\sin x\cdot0=\cos x\\\\\cos\left((\pi)/(2)-x\right)=\cos(\pi)/(2)\cos x+\sin(\pi)/(2)\sin x=0\cos x+1\sin x=\sin x`

`\sin\left((\pi)/(2)-x\right)\cos x+\cos\left((\pi)/(2)-x\right)\sin x\\\\=\cos x\cos x+\sin x\sin x=\cos^2x+\sin^2x=1`