Prove that
sin(x+y)_tan x +tan y
sin(x-y) tan x-tan y
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Solution :
L.H.S.=sin(x+y)sin(x−y)
=sinxcosy+sinycosxsinxcosy−cosxsiny
Dividing numerator and denominator by cosxcosy
=(sinxcosx)+(sinycosy)(sinxcosx)−(sinycosy)
=tanx+tanytanx−tany=R.H.S
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