SOLUTION: establish each identity A) sin theta times cos theta over cos^2 theta - sin^2 theta = tan theta over 1

SOLUTION: establish each identity A) sin theta times cos theta over cos^2 theta - sin^2 theta = tan theta over 1 - tan^2 theta

Question 701098: establish each identity
A) sin theta times cos theta over cos^2 theta - sin^2 theta = tan theta over 1 - tan^2 theta
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Rather than typing theta, I'll use x.
The left side has
(1) (sin x * cos x)/(cos^2 x - sin^2 x)
Now divide both numerator and denominator by cos^2 x and get
(2) (sin x /cos x)/(1-(sin^2 x /cos^2 x))
Using the identity
(3) tan x = sin x /cos x
we get the left side equals
(4) tan x/(1-tan^2 x)
which is the same as the given right side, thus demonstrating the identity.
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