Question

Prove that :sinx sin2x+sin 3x sin6x/sinx cos2x+sin 3x cos6x=tan5x

Answer 1

Step-by-step explanation:

Dear student

sinx sin2x+/sin3x sin6xsinx cos2x+sin3x cos6xMultiplying numerator and denominator by 2, we get=2sinx sin2x+2sin3x sin6x2sinx cos2x+2sin3x cos6x=cos(x−2x)−cos(x+2x)+cos(3x−6x)−cos(3x+6x)sin(x+2x)+sin(x−2x)+sin(3x+6x)+sin(3x−6x)=cos(−x)−cos3x+cos(−3x)−cos9xsin3x sin(−x)+sin9x+sin(−3x)=cosx−cos3x+cos3x−cos9xsin3x−sinx+sin9x−sin3x=cosx−cos9xsin9x−sinx=2sin(x+9x2)sin(9x−x2)2cos(x+9x2)sin(x−9x2)=sin5x sin4xcos5x sin(−4x)=tan5x (∵sin(−A)=−sinA

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