# ✅ 2cosacosb Formula ⭐️⭐️⭐️⭐️⭐

## 2cosacosb

Trigonometry is the field of study which deals with the relationship between angles, heights, and lengths of right triangles. The ratios of the sides of a right triangle is known as trigonometric ratios. Trigonometry has six main ratios namely sin, cos, tan, cot, sec, and cosec. All these ratios have different formulas. It uses the three sides and angles of a right-angled triangle. Let’s look into 2cosacosb formula in detail.

As we know that there are six Trigonometric functions of angles and their names are:

1. Sine
2. Cosine
3. Tangent
4. Cotangent
5. Secant
6. Cosecant

These functions are in relation to the right triangle in the following way:

In any right triangle ABC,

## What is 2cosacosb Formula?

Consider a right triangle ABC as shown below,

We know that,

sinθ = Opposite/Hypotenuse

• cos A = AB/AC
• cos B = BC/AC
• sin A = BC/AC
• sin B = AB/AC

We know that,

cos (A + B) = cos A cos B – sin A sin B ….. (1)

cos (A – B) = cos A cos B + sin A sin B ….. (2)

Adding (1) and (2), we get

cos (A + B) + cos (A – B) = 2 cos A cos B

For any two acute angles A and B in a right triangle the 2cosacosb formula is given by

## Formula of 2cosacosb

We know that,

cos (A + B) = cos A cos B – sin A sin B ….. (1)

cos (A – B) = cos A cos B + sin A sin B ….. (2)

Adding (1) and (2), we get

cos (A + B) + cos (A – B) = 2 cos A cos B

### Solved Examples using 2cosacosb Formula

Example 2: Express 6 cos x cos 2x in terms of sum function.
Solution:
Consider,
6 cos x cos 2x
= 3 [2 cos x cos 2x]

Using the formula 2 cos A cos B = cos (A + B) + cos (A – B),
= 3[cos (x + 2x) + cos (x – 2x)] = 3[cos 3x + cos (-x)] = 3 [cos 3x + cos x]

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### 2 Cos A Cos B Formula Application

Express 2 Cos 7x Cos 3y as a Sum

Solution:

Let A = 7x and B = 3y

Using the formula:

2 Cos A Cos B = Cos (A + B) + Cos (A – B)

Substituting the values of A and B in the above formula, we get

2 Cos A Cos B = Cos (7x + 3y) + Cos (7x – 3y)

2 Cos A Cos B = Cos 10x + Cos 4y

Hence, 2 Cos 7x Cos 3y = Cos 10x + Cos 4y