Question

verify that sin 2 theta = 2 sin theta cos theta

Answer 1

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Answer 2

Given:

sin 2Ф = 2 sinФ cosФ

To Find:

Verify above expression

Solution:

As we know,

Sin( A + B ) = sinA cosB +sinB cosA

Now we can write,

sin 2Ф = sin ( Ф + Ф )

so according to formula,

sin ( Ф + Ф ) = sinФ cosФ +sinФ cosФ

sin ( Ф + Ф ) = 2 sinФ cosФ

∴  sin 2Ф = 2 sinФ cosФ

Hence proved.