Answers

2016-05-07T10:14:18+05:30
Solutions 

LHS= 2sin((3x+2x)/2)cos((3x-2x)/2)-sinx


                 sin (a+b) = 2sin((a+b)/2)cos((a-b)/2)


       = 2sin(5x/2)cos(x/2)-sinx           we have sin2x=2sinxcosx
                                                              similarly sinx=2sin(x/2)cos(x/2)

       = 2sin(5x/2)cos(x/2) - 2sin(x/2)cos(x/2)

       = 2cos(x/2)[sin(5x/2) - sin(x/2)]

       = 2cos(x/2)*2cos(3x/2)sin(x)       [sin (a-b) = 2cos((a+b)/2)sin((a-b)/2)

       = 4sin(x)cos(x/2)cos(3x/2) = RHS
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