Prove the following: sin 2x = (tan x)(1 + cos 2x)

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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 +...

Unlock
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Start your 48-Hour Free Trial

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)

 

Approved by eNotes Editorial Team