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Question
Prove that:
sin 60° = 2 sin 30° cos 30°
Theorem
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Solution
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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