Question

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

Answer 1

`\tan\left(x+(\pi)/(2)\right)=-\cot x\\\\We\ know:\\\\\sin\left(x+(\pi)/(2)\right)=\cos x\\\\\cos\left(x+(\pi)/(2)\right)=-\sin x\\\\\tan x=(\sin x)/(\cos x)\\\\\cot x=(\cos x)/(\sin x)\\---------------\\\L=\tan\left(x+(\pi)/(2)\right)=(\sin\left(x+(\pi)/(2)\right))/(\cos\left(x+(\pi)/(2)\right))=(\cos x)/(-\sin x)=-\cot x=R\\\\\boxed{ }`