Question

Question #d73e5

Answer 1

See explanation.

Explanation:

Well, let's see what we can do starting from the left-hand-side.
I see I can transform the `tan x` the following way:
`sin x tan x = sin x (sin x)/(cos x) = (sin^2 x)/(cos x)`
Now, we see we're getting closer since we already have the `1/cos x` part.
Let's now transform `sin^2 x`.
We recall the identity `sin^2 x + cos^2 x = 1`.
This becomes `sin^2 x = 1 - cos^2 x`. So we can now rewrite our equation:
`sin x tan x = (sin^2 x)/(cos x) = (1- cos^2 x)/(cos x)`
Simplifying, we have:
`sin x tan x = (1)/(cos x) - (cos^2 x)/(cos x)`
and cancelling out the `cos x` in the rightmost term, we get:
`sin x tan x = (1)/(cos x) - cos x`
Q.E.D.