Use identities to rewrite tan^2 x(1 + cot^2 x) in terms of sin x and cos x. Then simplify so that no quotients appear.

Question

My way of going about this was to use the double angle identity for tangent but there's 3 formulas for it.

tan2x

=2tanx/1-tan2 x

=2cotx/cot2 x-1

= 2/cot x – tan x

I don't understand how to figure out which one to use and how to plug the problem into the formula.

Answer 1

tan²x(1 + cot²x) = tan²x + tan²xcot²x = tan²x + 1 = sec²x = 1/cos²x