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 (\sin (x+y))/(\sin (x-y))\\\\\Rightarrow (\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 (( \sin x \cos y)/(\cos x \cos y) +( \sin y \cos x)/(\cos x \cos y))/(( \sin x \cos y)/(\cos x \cos y) -( \sin y \cos x)/(\cos x \cos y))\\\\\Rightarrow (\tan x +\tan y)/(\tan x -\tan y)`

Answer 2

`(sin(x+y))/(sin(x-y)) = (tan(x)+tan(y))/(tan(x)-tan(y))`