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सिद्ध कीजिए कि `sin20^(@)sin40^(@)sin60^(@)sin80^(@)=(3)/(16)` |
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Answer» बायाँ पक्ष `" "=sin 20^(@) sin 40^(@) sin 60^(@) sin 80^(@)` `=sin 20^(@) sin 40^(@)(sqrt3)/(2)sin80^(@)" "(because sin 60^(@)=(sqrt3)/(2))` `=(sqrt3)/(2)[(1)/(2){cos(40^(@)-20^(@))-cos(40^(@)+20^(@))}]sin 80^(@)` `=(sqrt3)/(2)xx(1)/(2)(cos 20^(@)-cos60^(@))sin 80^(@)` `=(sqrt3)/(4)(cos 20^(@)sin 80^(@)-cos 60^(@) sin 80^(@))` `=(sqrt3)/(4) [(1)/(2){sin(20^(@)+80^(@))-sin (20^(@)-80^(@))}-(1)/(2)sin 80^(@)]" "(because cos 60^(@)=(1)/(2))` `=(sqrt3)/(4)xx(1)/(2)[sin 100^(@)-sin(-60^(@))-sin 80^(@)]` `=(sqrt3)/(8)[sin(180^(@)-80^(@))+sin 60^(@)-sin 80^(@)]` `=(sqrt3)/(8)[sin 80^(@)+sin 60^(@)-sin 80^(@)]` `=(sqrt3)/(8)sin 60^(@)` `=(sqrt3)/(8)xx(sqrt3)/(2)` `=(3)/(16)=` दायाँ पक्ष |
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