2cosacosb Formula
Formula of 2 cosa cosb : As we know that there are 6 trigonometric functions and they named as following – sine, cosine, tangent, cotangent, secant, and cosecant. These trigonometric functions have different formulas and can be related to each other in right triangle. Three sides of right angled triangle is mainly used by these 6 trigonometric functions sine, cosine, tangent, cotangent, secant, and cosecant.
| Sin A = Perpendicular/ Hypotenuse |
| Cos A = Base/ Hypotenuse |
| Tan A = Perpendicular/ Base |
| Cot A = Base/ Perpendicular |
| Cosec A = Hypotenuse/Perpendicular |
| Sec A = Hypotenuse/ Base |
What is 2 cosa cosb Formula?
This 2 cos A cos B or 2 cosa cosb formula can be used to solve such integration formulas which involving the product, addition, subtraction of trigonometric ratio. The formula of 2cosacosb is very helpful to convert some trigonometric formulas from product form to addition form such as cos (A + B) + cos (A – B) = 2 cos A cos B.
IF you want to drive this 2 cosa cosb formula then you must know two important trigonometric identities cos (A + B) = cos A cos B – sin A sin B and cos (A – B) = cos A cos B + sin A sin B. From these two trigonometric identities we can easily drive the 2cosacosb formula.
- cos (A + B) = cos A cos B – sin A sin B ….. (1)
- cos (A – B) = cos A cos B + sin A sin B ….. (2)
After Adding Equation (1) and (2), we will get the following expression cos (A + B) + cos (A – B) = 2 cos A cos B. Please follow this link of Explanation of Mathematics formula – Click
2cosacosb Formula Solved examples
Example 1: Express 8 cos y cos 2y in terms of sum cosine function.
- Solution: 8 cos y cos 2y=
- 4 [2 cos y cos 2y]
- Using the 2cosa cosb Formula, 2 cos A cos B = cos (A + B) + cos (A – B)
- = 4[cos (y + 2y) + cos (y – 2y)]
- rewrite as 4[cos 3y + cos (-y)]
- = 4 [cos 3y + cos y]
- Thus, 8 cos y cos 2y in terms of sum function is 4 [cos 3y + cos y].
Example 2: Express 2 Cos 7x Cos 3y as a Sum of cosine function
- Solution: Let us assume 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
FAQs
We know that cos (A + B) + cos (A – B) = 2 cos A cos B by using this formula we can get cos a cos b = (1/2)[cos(a + b) + cos(a – b)]
2 sin a cos a = sin 2a
cos a cos b = (1/2)[cos(a + b) + cos(a – b)]
2 sinA cosB = sin(A + B) + sin(A − B)
2 Cos A Cos B = Cos (A + B) + Cos (A – B)
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