SOLUTION: Prove that tan(pi/2+x)=-cotx

Question 196590: Prove that tan(pi/2+x)=-cotx
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Note: I'm ONLY manipulating the left side.

Use the identity

Expand

Note: and

Evaluate the sine of to get 1. Evaluate the cosine of to get 0

Multiply

Simplify

Use the identity

So this verifies the identity
RELATED QUESTIONS
prove the co-function identity tan(x+ pi/2) =... (answered by Theo)

prove using the t = tan (x/2) [tan 2x + cotx] / [tan2x - tanx] - cot^2... (answered by ikleyn)

cotx-tan^2=0 (answered by Alan3354)

Prove that: tanx +tan(x+pi/3)... (answered by Edwin McCravy)

Prove the identity i) cotx - cot2x = cosec2x ii) Show that *integral* (with limit pi/4 (answered by ikleyn)

Prove the identity i) cotx - cot2x = cosec2x ii) Show that *integral* (with limit pi/4 (answered by Edwin McCravy,mccravyedwin,AnlytcPhil)

prove that tan x(cot x + tan x) = sec^2 x. Prove this for ANY... (answered by venugopalramana)

Prove that the identity is true {{{ tan(x)^3= tan(x)sec(x)^2-tan(x)... (answered by lwsshak3)

If {{{tan(3x) tan (2x) = tan (pi/4)}}}, find the value of {{{sin(5x)}}}, given that {{{0... (answered by ikleyn)