** Cos square x integration**

What is Integration of cos square x dx ? In this article we will derive the integral of cosine squared x – Solving the Integral of cos^{2}x. ∫cos^{2}x dx = ? So Directly we can not just integrate cos^{2}x. We have to convert cos^{2}x into another form by using trigonometric identities to find the integration.

This integration of cos^{2} x dx cannot be evaluated by the directly by using any formula or integration formula, so we have to use trigonometric identity of half angle cos square x or cos^{2} x = (1+cos2x) / 2.

- I = ∫cos
^{2}x dx - I =∫{(1+cos2x)/2} dx
- ⇒ I = (1/2)∫(1+cos2x) dx
- ⇒ I = (1/2) ∫1dx + (1/2) ∫cos2x dx
- Using the integral formula ∫cos kx dx = (sin kx) / k+c, we have

∫cos^{2}x dx = (1/2) x + (1/2) (sin2x) / 2 + c - ⇒ ∫cos
^{2}x dx = (1/2) x +(1/4) (sin2x) + c, where C is integration constant

**Integration of cos square x by using double angle formula**

The double angle trigonometric identity formula: cos 2x = cos^{2} x – sin^{2} x. There is one more trigonometric identity which will be very useful to find integration of cos square x. Second trigonometric identity is sin^{2} x + cos^{2} x = 1. Now we have to combine these both trigonometric identities cos 2x = cos^{2} x – sin^{2} x and sin^{2} x + cos^{2} x = 1. After combining we will get cos 2x = 2cos^{2} x -1.

- cos 2x = 2cos
^{2}x -1 - After rearranging cos
^{2}x = ( 1+ cos 2x ) / 2, Now we can use reverse chain rule to integrate this expression. - We will get x/2 + ( sin 2x ) / 4 + c, where C is a integration constant.

Please follow this link of Explanation of Mathematics formula – **Click**

**What is the formula of Cos Square x?**

**cos ^{2}x = 1 – sin^{2}x**

**What is the value of Cos Square θ?**

cos^{2}θ = 1 – sin^{2}θ

**Can you integrate cos 2 x?**

Yes, but we have to change it in another form by using trigonometric identities cos 2x = cos^{2} x – sin^{2} x and sin^{2} x + cos^{2} x = 1. From these trigonometric identities we will get cos 2x = 2cos^{2} x -1.

**How do you integrate Cos X?**

**∫ cos x dx = sin x + C**

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