Question

Prove that:

sin 60° = 2 sin 30° cos 30°

Answer 1

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°