How do u prove this ?

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1 Answer
Apr 17, 2018

Kindly go through a Proof in the Explanation.

Explanation:

sin(120^@+alpha)=sin{180^@-(60^@-alpha)},

=sin(60^@-alpha),

=sin60^@cosalpha-cos60^@sinalpha.

rArr sin(120^@+alpha)=1/2(sqrt3cosalpha-sinalpha)......(1).

Similarly, sin(120^@-alpha)=sin(60^@+alpha).

:. sin(120^@-alpha)=1/2(sqrt3cosalpha+sinalpha)......(2).

"From "(1) and (2),

sin^2alpha+sin^2(120^@+alpha)+sin^2(120^@-alpha),

=sin^2alpha+1/4(sqrt3cosalpha-sinalpha)^2+1/4(sqrt3cosalpha+sinalpha)^2,

=sin^2alpha+1/4{2(3cos^2alpha+sin^2alpha)}..........[because, (a+b)^2+(a-b)^2=2(a^2+b^2)],

=sin^2alpha+3/2cos^2alpha+1/2sin^2alpha,

=3/2sin^2alpha+3/2cos^2alpha,

=3/2, as desired!

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