Question

Difference of Squares in Trigonometric Functions
\[\frac{ 3tanx }{ 1+\tan^2 }=3sinxcosx\]

Answer 1

Are you trying to prove that the LHS = RHS ?

Answer 2

Yes

Answer 3

ok.

Answer 4

what are you stuck with? Do you understand how to approach this problem?

Answer 5

I mean, I understand that you need to factor in order to solve it but I don't know where to start

Answer 6

\[(3tanx)/(1+\tan^2x) = 3sinxcosx\]
\[Since, tanx = sinx/cosx\]
We can do the following:
\[3sinx/cosx/(1+ \sin^2x/\cos^2x)\]

Answer 7

then find a common denominator which is cos^x

Answer 8

\[3sinx/cosx * \cos^2x / \cos^2x+\sin^2x\]
Then we notice that cos^2 + sinx^2 = 1 <- which is the Pythagorean identity.

Answer 9

then after more algebraic simplification we get 3sinxcosx

Answer 10

Ahh thank you!

Answer 11

thus both sides match and the identity holds.

Answer 12

Your welcome.