Question

Drag each label to the correct location on the expression. Each label can be used more than once, but not all labels will be used. Complete this equation. __________

Answer 1

Answer with explanation:

→sin (x+y)=sin x cos y +cos x sin y

→sin (x-y)= sin x cos y - cos x sin y

$\Rightarrow \frac{\sin (x+y)}{\sin (x-y)}\\\\\Rightarrow \frac{\sin x \cos y + \cos x \sin y}{\sin x \cos y - \cos x \sin y}\\\\\rightarrow \text{Dividing numerator and Denominator by} \cos x \cos y\\\\ \Rightarrow \frac{\frac{ \sin x \cos y}{\cos x \cos y} +\frac{ \sin y \cos x}{\cos x \cos y}}{\frac{ \sin x \cos y}{\cos x \cos y} -\frac{ \sin y \cos x}{\cos x \cos y}}\\\\\Rightarrow \frac{\tan x +\tan y}{\tan x -\tan y}$

Answer 2

$\frac{sin(x+y)}{sin(x-y)} = \frac{tan(x)+tan(y)}{tan(x)-tan(y)}$