Question

If 1 + cos 2x = 2cos²x then 1 + cosx = ? Kindly explain it in detail.

Answer : 2cos²(x/2)

Answer 1

Answer:

This is the proof of above question

Step-by-step explanation:

hope it'll help you

Answer 2

Topic :-

Trigonometric identities and expansions

Given :-

1 + cos 2 x = 2 cos² x

To find :-

1 + cos x

Solution :-

Since in the given identity, we are given the value of 1 + cos 2 x and we are asked to find the value of 1 + cos x.

This seems to be somewhat straight forward question. It's clear that if we substitute value of 2x = x in the given identity, we would get our desired result.

We will start our question by substituting 2x = x.

$\longrightarrow1 + \cos \left(2x\right) = 2 { \cos}^{2}\left(x\right)$

or,

${ \longrightarrow1 + \cos \left(2x \right) = 2 { \cos}^{2} \left( \dfrac{2x}{2} \right)}$

Now substitute 2x = x

${ \longrightarrow1 + \cos \left(x \right) = 2 { \cos}^{2} \left( \dfrac{x}{2} \right)}$

This is the required result.

Learn More formulas :-

• 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