Question

How can I solve this?

`sec^2x cotx - cotx = tanx`

Answer 1

I just used the fact that secant is one over cosine, cotangent is cosine over sine, and tangent is sine over cosine, and that cos^2 x + sin^2 x = 1.

Explanation:

`(1/cos^2 x)(cos x/sin x)-(cos x/sin x)`
`(1/(cos x sin x)) - (cos x/sin x)`

Give them a common denominator.

`((1 - cos^2 x)/(cos x sin x)) = (sin ^2 x/(cos x sin x)) = (sin x/cos x) = tan x`