Question

"True or false: Explain. tan(x + π/2) = -cot(x) for all x ≠ πk for an integer k"

Can someone explain to me how I would go about doing this? I think I need to use a sum or difference of two angles formula, but I don't know how to do that with tan.

Answer 1

well... grab the 2 given angles and use them in the tangent sum/difference identity \(\bf tan(\alpha\pm beta)=\cfrac{tan(\alpha)\pm tan(\beta) }{1\mp tan(\alpha)tan(\beta)}\)

Answer 2

Ooohh, I see! Thank you so much!

Answer 3

\(\bf {\color{brown}{ tan(\alpha\pm beta)=\cfrac{tan(\alpha)\pm tan(\beta) }{1\mp tan(\alpha)tan(\beta)}}}
\\ \quad \\ \quad \\
tan\left(x+{\color{blue}{ \frac{\pi}{2}}}\right)=\cfrac{tan\left({\color{blue}{ \frac{\pi}{2}}}\right)+tan(x)}{1-tan\left({\color{blue}{ \frac{\pi}{2}}}\right)tan(x)}\)

Answer 4

hmm got them backwards.. a bit... but shouldn't matter... but anyhow \(\bf {\color{brown}{ tan(\alpha\pm beta)=\cfrac{tan(\alpha)\pm tan(\beta) }{1\mp tan(\alpha)tan(\beta)}}}
\\ \quad \\ \quad \\

tan\left(x+{\color{blue}{ \frac{\pi}{2}}}\right)=

\cfrac{tan(x)+tan\left({\color{blue}{ \frac{\pi}{2}}}\right)}{1-tan(x)tan\left({\color{blue}{ \frac{\pi}{2}}}\right)}\)

Answer 5

yw