help with tan x question

Question

 

how do I prove that tan  x (cot x + tan x) = sec^2 x

 

thank you

Answer 1

tan(x)[cot(x) + tan(x)] = sec²(x)

 

Identity: cot(x) = 1/tan(x)

 

tan(x)[(1/tan(x)) + tan(x)] = sec²(x)

 

tan(x)/tan(x) + tan²(x) = sec²(x)

 

1 + tan²(x) = sec²(x)

 

which is a Pythagorean identity.