Mathematics
Lexi324
21

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

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(1) Answers
MickieGelormino111

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

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