Question

How do you prove (sinx)(cosx)(tanx) + cos2x = 1 ?

Answer 1

We have:

`sinx(cosx)(sinx/cosx) + cos(2x) = 1`

`sin^2x + 1 - 2sin^2x = 1`

`-sin^2x = 0`

`sinx = 0`

`x = 0 or pi ->x= pin`

Hopefully this helps!

Answer 2

`f(x) = (sin x)(cos x) (sin x/cos x) + cos 2x =`
`= sin^2 x + cos 2x`.
Replace cos 2x by `(cos^2 x - sin^2 x)`
`f(x) = sin^2 x + cos^2 x - sin^2 x = cos^2 x`
The equation `f(x) = cos^2 x = 1` is impossible, except when
`cos^2 x = 1` --> `cos x = +- 1` -->
`x = kpi`