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Question

If sin x + sin y = 3 (cos y − cos x), then sin 3x + sin 3y =
(a) 2 sin 3x
(b) 0
(c) 1
(d) none of these


Solution

We have,
sin x + sin y = 3 (cos y − cos x)

2sinx+y2 cosx-y2 = 23sinx+y2 sinx-y22sinx+y2cosx-y2-23sinx+y2sinx-y2=02sinx+y2cosx-y2-3sinx-y2=0sinx+y2cosx-y2-3sinx-y2=0sinx+y2=0 or, cosx-y2-3sinx-y2=0x+y2=0       or, tanx-y2=13=tanπ6x=-y             or, x-y2=π6x=-y             or, x-y=π3
Case-I
When x=-y
In this case,
sin3x+sin3y=sin-3y+sin3y=-sin3y+sin3y=0
Case-II 
when x-y=π3
or, 3x=π+3ySo, sin 3x+sin 3y= sinπ+3y+sin 3y                               =-sin 3y+sin 3y                               =0   

Mathematics
RD Sharma XI (2015)
Standard XI

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