Prove that sin20sin40sin80=under root 3/8
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L.H.S=sin20(sin40.sin80)
=sin20/2 (2sin40.sin80)
=sin20/2 (cos40-cos120)
=sin20/2 (cos40-cos60)
=1/2 (sin20cos40+1/2sin20)
=1/2 (2sin20cos40/2 +1/2sin20)
=1/4 (sin60-sin20+sin20)
=1/4×root3/2
=under root 3/8
=R.H.S
=sin20/2 (2sin40.sin80)
=sin20/2 (cos40-cos120)
=sin20/2 (cos40-cos60)
=1/2 (sin20cos40+1/2sin20)
=1/2 (2sin20cos40/2 +1/2sin20)
=1/4 (sin60-sin20+sin20)
=1/4×root3/2
=under root 3/8
=R.H.S
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