Learn Prove Cos 3x 4cos3x 3cosx

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# Prove cos 3x = 4cos3x−3cosx

We can prove cos 3x = 4cos3x−3cosx using trigonometric identity

## Answer: cos 3x = 4cos3x−3cosx

Let us see how we can prove this.

**Explanation:**

cos 3x can be written as cos3x = cos(2x+x)—–(i)

As we know the trigonometric identity: cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

Applying the trigonometric identity to equation (i) and we get,

cos 3x = cos2x cosx − sin2x sinx

= (−1+2cos^{2}x)cosx − 2cosx sinx sinx

= −cosx+2cos^{3}x − 2sin^{2}x cosx

= −cosx+2cos ^{3}x − 2(1−cos^{2}x)cosx

= −3cosx + 4cos^{3}x

= 4cos^{3}x − 3cosx

### Hence, cos 3x = 4cos3x−3cosx

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