Question #0912d

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Answer 1 · 2016-12-20T14:37:40

#LHS=sin ^2 theta + sin^2 (theta+pi/3) + sin^2 (theta-pi/3)#

#=1/2(2sin ^2 theta + 2sin^2 (theta+pi/3) + 2sin^2 (theta-pi/3)#

#=1/2(1-cos2 theta + 1-cos2 (theta+pi/3) + 1-cos2 (theta-pi/3)#

#=1/2(3-cos2 theta -(cos2 (theta+pi/3) + cos2 (theta-pi/3))#

#=1/2(3-cos2 theta -2cos2 thetacos((2pi)/3))#

#=1/2(3-cos2 theta -2cos2 thetaxx(-1/2))#

#=3/2=RHS#

Proved