Question

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

Answer 1

So far i have: \[ (\tan(x) + \tan(\pi/2)) / (1 - \tan(x)\tan(\pi/2))\]

Answer 2

\[\tan(x +\frac{ \pi }{ 2 })=\frac{ \sin(x+\frac{ \pi }{ 2 } )}{ \cos(x+\frac{ \pi }{ 2 } )}\]
\[=\frac{ \sin x \cos \frac{ \pi }{ 2}+\cos x \sin \frac{ \pi }{ 2 } }{ \cos x \cos \frac{ \pi }{ 2 }-\sin x \sin \frac{ \pi }{ 2 } }\]

Answer 3

Okay, I know how you got there, but after that, how do you simplify to -cot(x)?

Answer 4

@peachpi

Answer 5

cos(π/2) = 0 and sin (π/2) = 1, so it simplifies to

\[\frac{ 0+\cos x }{ 0-\sin x }=-\frac{ \cos x }{ \sin x }=-\cot x\]