Question

Solve sin2theta=2sinthetacostheta​

Answer 1

`\sin(2\theta) =2 \sin \theta \cos \theta` proved

Explanation:

Given

`\sin2 \theta=2 \sin\theta cos\theta`

Required

Prove

Proving from left to right.

`\sin(2\theta) = \sin(\theta+\theta)`

In trigonometry

`\sin(A+B) = \sin A \cos B+\sin B \cos A`

When this formula is applied to:
`\sin(2\theta) = \sin(\theta+\theta)`

We have:

`\sin(2\theta) = \sin \theta \cos \theta+\sin \theta \cos \theta`

`\sin(2\theta) =2 \sin \theta \cos \theta`

Proved