The identity to be proved is sin 2x = (tan x)(1 + cos 2x)

Let's start from the right hand side

(tan x)(1 + cos 2x)

use tan x = sin x / cos x and cos 2x = 2(cos x)^2 - 1

=> (sin x / cos x)(1 +...

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The identity to be proved is sin 2x = (tan x)(1 + cos 2x)

Let's start from the right hand side

(tan x)(1 + cos 2x)

use tan x = sin x / cos x and cos 2x = 2(cos x)^2 - 1

=> (sin x / cos x)(1 + 2*(cos x)^2 - 1)

=> (sin x)(2*cos x / cos x)

=> 2*sin x*cos x

=> sin 2x

which is the left hand side

**This proves the identity is sin 2x = (tan x)(1 + cos 2x)**