How do u prove this ?

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Answer 1 · 2018-04-17T19:38:04

Kindly go through a Proof in the 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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