Question

How do you write the expression `(tan2x+tanx)/(1-tan2xtanx)` as the sine, cosine, or tangent of an angle?

Answer 1

`tan3x=sin(3x)/cos(3x).`

Explanation:

Recall the Identity :

`tan(A+B)=(tanA+tanB)/(1-tanAtanB).`

With `A=2x, and, B=x`, it follows that,

`"The Exp.="tan(2x+x)=tan3x=sin(3x)/cos(3x).`