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one of the general solution of the equation 4sinx.sin2x.sin4x-sin3x is

one of the general solution of the equation
4sinx.sin2x.sin4x-sin3x is

Grade:12

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
8 years ago
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Amar Sharma
11 Points
7 years ago
2(2sinx sin2x) sin4x = sin 3x2 (cosx - cos3x) sin4x = sin 3x2cosxsin4x -2cos3xsin4x =sin3xsin(4x+x)+sin(4x-x)-sin(4x+3x)-sin(4x-3x)=sin3xsin5x+sin3x-sin7x-sinx=sin3xsin5x-sin7x=sinx-2cos6x-sinx=sinx(1+2cos6x)sinx=0Now,Either sinx =0 or (1+2cos6x)=0Therefore, x=npi or x=1/6(2npi +_ pi/3)

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