The cos^3x formula is given by cos^{3}x = (cos3x + 3cosx)/4. In this post, we learn how to prove the cos cube x formula.

## What is cos cube x formula

Answer: cos^{3}x=(cos3x + 3cosx)/4 is the formula of cos cube x. |

*Proof:*

We will follow the below steps in order to prove cos cube x formula.

**Step 1:** First, we use cos3x formula and the formula is given below:

cos3x = 4cos^{3}x – 3cos x.

**Step 2:** Now we add 3cosx to both sides of the above equation. By doing so, we obtain that

cos3x + 3cox= 4cos^{3}x – 3cos x +3cosx.

⇒ cos3x + 3cox = 4cos^{3}x …(I)

**Step 3:** Dividing both sides of (I) by 4, we have that

(cos3x + 3cosx)/4 = cos^{3}x.

Therefore, the cos^{3}x formula is obtained as follows: cos^{3}x = (cos3x + 3cosx)/4.

*Remark:*

Replacing x in the above formula by θ, the formula of cos^{3}θ (cos cube theta) is given by cos^{3}θ = (cos3θ + 3cosθ)/4.

**Have You Read These?**

Sin3x Formula | Cos3x Formula |

sin^{3}x Formula | sinx siny Identity |

tan(x-y) Formula | cot(x+y) Formula |

Simplify sin(cos^{-1}x) | cos^{2}x-sin^{2}x Formula |

## FAQs

**Q1: What is the cos^3x formula?**

**Answer:** The cos^3x formula states that cos^{3}x =(cos3x + 3cosx)/4.

**Q2: What is the cos^3θ formula?**

**Answer:** The cos cube theta formula is given by cos^{3}θ = (cos3θ + 3cosθ)/4.