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prove that sin20+sin40-sin80=0?
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Verified answer
L .H.S. = sin20+ sin40 - sin 80
= 2 sin(20+40)/2 cos (40-20)/2 - sin80
= 2 sin30 cos10 - sin 80
=2x1/2 cos10 - sin80
= cos10 - sin(90- 10)
=cos10 - cos10
= 0=R.H.S.
sinA-sinB=2cos[(A+B)/2]sin[(A-B)/2] with A=40 and B=80 gives
sin40-sin80=2cos60sin(-20)=2(1/2)(-sin20)=-sin20 and you get the result.