Question

If 1 + cos 2x = 2cos²x then 1 + cosx =

Answer 1

Given : 1 + cos 2x = 2 cos²x

To find : Value of 1 + cos 2x

Solution :

We are given the value of 1 + cos 2x and we are asked to find the value of 1 + cos x. If we divide the angle by 2, we will get our desired result.

So put the value of x = x / 2

=> 1 + cos 2x = 2 cos² x

=> 1 + cos[ 2 ( x / 2 ) ] = 2 cos² ( x / 2 )

=> 1 + cos x = 2 cos² x/2

So the required answer is 2 cos² x/2.

Additional Information :-

• cos ( A + B ) = cos A. cos B - sin A. sin B
• cos ( A - B ) = cos A. cos B + sin A. sin B
• sin ( A + B ) = sin A. cos B + cos A. sin B
• sin ( A - B ) = sin A. cos B - cos A. sin B
• sin 2x = 2 sin x. cos x
• cos 2x = cos²x - sin²x
• cos 2x = 1 - sin²x
• sin 3x = 3 sin x - 4 sin³x
• cos 3x = 4 cos³x - 3 cos x

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