Question

Prove that: tanx(cot x+tan x)=sec^2x

Answer 1

Using the fact that :
\[\cot(x) = \frac{1}{\tan(x)}\]
when we multiply that out we get:
\[\tan(x)(\frac{1}{\tan(x)})+\tan^{2}(x) = 1+\tan^{2}(x) = \sec^{2}x\]

Answer 2

tanx(cot x+tan x) = 1 + tan^2 x = sec ^2x

Answer 3

the\[1+\tan^{2}(x) = \sec^{2}(x) \]
comes from this equation:
\[\sin^{2}(x)+\cos^{2}(x) = 1\]
and dividing everything by cos^2(x)