Question

How do you perform addition or subtraction and use the fundamental identities to simplify `tanx-sec^2x/tanx`?

Answer 1

• cot x

Explanation:

`f(x) = tan x - sec^2 x/(tan x)`
`f(x) = sin x/(cos x) - (1/(cos^2 x))(cos x/(sin x))`
`f(x) = (sin x/(cos x)) - (1/(sin x.cos x)) = (sin^2 x - 1)/(sin x.cos x)`
`f(x) = - (cos^2 x)/(sin x.cos x) = - cos x/(sin x) = cot x`