Question

Verify the identity.
tan (x + pi/2) = -cot x

Answer 1

`\tan\left(x+\frac\pi2\right)=(\sin\left(x+\frac\pi2\right))/(\cos\left(x+\frac\pi2\right))=(\sin x\cos\frac\pi2+\cos x\sin\frac\pi2)/(\cos x\cos\frac\pi2-\sin x\sin\frac\pi2)=(\cos x)/(-\sin x)=-\cot x`