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

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Answer 1 · 2018-03-13T05:33:32

Kindly go through the Explanation.

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

#=2sin[{(x+y)+(x-y)}/2]cos[{(x+y)-(x-y)}/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!