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

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Question 329976: Prove that tan x (cot x + tan x) = sec^2x
Answer by mathslover(157) About Me  (Show Source):
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Prove that tan x (cot x + tan x) = sec^2x
LHS (Left hand side)
tan x (cot x + tan x)
=tan x * cot x + (tan x)(tan x)
=1+ tan^2 x
=1 + sin^2 x/cos ^ x
=(cos ^ 2 x + sin ^ x)/cos ^2 x
=1/cos^2 x
=sec ^2 x = RHS (right hand side)