Question #d73e5

1 Answer
Feb 3, 2018

Answer:

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.