Sin (x+y) + sin (x-y) / sin (x+y) - sin (x-y) = tan x cot y ?

1 Answer
Mar 13, 2018

Kindly go through the Explanation.

Explanation:

sin(x+y)+sin(x-y)sin(x+y)+sin(xy),

=2sin[{(x+y)+(x-y)}/2]cos[{(x+y)-(x-y)}/2]=2sin[(x+y)+(xy)2]cos[(x+y)(xy)2],

:. sin(x+y)+sin(x-y)=2sinxcosy......(ast^1).

Otherwise,

sin(x+y)+sin(x-y),

=(sinxcosy+cosxsiny)+(sinxcosy-cosxsiny),

=2sinxcosy.

Similarly, sin(x+y)-sin(x-y)=2cosxsiny......(ast^2).

From (ast^1) and (ast^2), we have,

{sin(x+y)+sin(x-y)}/{sin(x+y)-sin(x-y)}=(2sinxcosy)/(2cosxsiny),

=(sinx/cosy)*(cosy/siny),

=tanxcoty, as desired!