read the proof. what is the missing step and reason? step reason =(tan(x)+tan(x))/(1 - tan(x)tan(x))…

read the proof. what is the missing step and reason? step reason =(tan(x)+tan(x))/(1 - tan(x)tan(x)); tangent double - angle identity tan(2x)=tan(x + x) addition =(tan(x)+tan(x))/(1 - tan(x)tan(x)); tangent sum identity? =(tan(x)+tan(x))/(1 + tan(x)tan(x)); tangent double - angle identity? =(tan(x)+tan(x))/(1 + tan(x)tan(x)); tangent sum identity =(2(x))/(1 - tan²(x)) simplify

read the proof. what is the missing step and reason? step reason =(tan(x)+tan(x))/(1 - tan(x)tan(x)); tangent double - angle identity tan(2x)=tan(x + x) addition =(tan(x)+tan(x))/(1 - tan(x)tan(x)); tangent sum identity? =(tan(x)+tan(x))/(1 + tan(x)tan(x)); tangent double - angle identity? =(tan(x)+tan(x))/(1 + tan(x)tan(x)); tangent sum identity =(2(x))/(1 - tan²(x)) simplify

Answer

Explanation:

Step1: Recall tangent sum - identity

The tangent sum - identity is $\tan(A + B)=\frac{\tan(A)+\tan(B)}{1 - \tan(A)\tan(B)}$. When $A = B=x$, we have $\tan(x + x)=\frac{\tan(x)+\tan(x)}{1-\tan(x)\tan(x)}$.

Step2: Simplify the numerator

$\tan(x)+\tan(x)=2\tan(x)$. So $\frac{\tan(x)+\tan(x)}{1 - \tan(x)\tan(x)}=\frac{2\tan(x)}{1-\tan^{2}(x)}$.

Answer:

$\tan(2x)=\frac{\tan(x)+\tan(x)}{1 - \tan(x)\tan(x)}$; tangent sum identity