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Prove that: sin 60° = 2 sin 30° cos 30° - Mathematics

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प्रश्न

Prove that:

sin 60° = 2 sin 30° cos 30°

सिद्धांत
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उत्तर

sin 60 = 2 sin 30 cos 30

`sin60^\circ = sqrt3/2`

`sin30^\circ = 1/2`

`cos 30^\circ = sqrt3/2`

`2  sin 30^\circcos^\circ = 2 xx 1/2xxsqrt3/2`

2 sin 30 cos 30 = 2 × `1/2xxsqrt3/2`

`\cancel2 xx 1/\cancel2 xx sqrt3/2 = sqrt3/2`

sin 60° = 2 sin 30° cos 30° 

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