Question

Prove that this equation is an identity:
tan(x){cot(x)+tan(x)}=sec^2(x)

Answer 1

\[\tan x(\cot x+\tan x)=\tan x \left( \frac{1}{tanx}+tanx \right)=1+ \tan^{2} x=\sec ^{2}x\]

Answer 2

STEPS
1. tan is reciprocal of cot
2. distribution
3. pythagorean identity

Answer 3

thanks