Basics of 2 cos a cos b Formula
The 2cosA cosB Formula is a useful tool when solving integration equations involving trigonometric ratios
2cosA cosB Formula
The 2cosA cosB Formula is a useful tool when solving integration equations involving trigonometric ratios. The formula works by adding the product of two cosines (one with the sum of two angles and the other with the difference of two angles) together. In other words, cos (A - B) = cos (A - B).
The formula is also known as the sin2x formula. The two sin x values are referred to as sin2x and tan2x. This formula is also known as the double angle sine function formula. It is a key factor in calculating angles. You can apply the formula to a variety of applications, from calculating a sine function to solving problems. To learn how to apply the 2cosacosb Formula, For example:
- 2 cos (2x) cos (2y) = cos (2x + 2y) + cos (2x - 2y)
- 2 cos (x/2) cos (y/2) = cos (x/2 + y/2) + cos (x/2 - y/2)
Solved example of 2 cos a cos b Formula
Example 1: Express 8 cos y cos 2y in terms of sum 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)]
= 4[cos 3y + cos (-y)]
= 4 [cos 3y + cos y]
Answer:
Thus, 8 cos y cos 2y in terms of sum function is 4 [cos 3y + cos y].
Example 2: Write 20 cos x cos 4x as sum.
Solution:
20 cos x cos 4x
= 10 [2 cos x cos 4x]
Using the 2cosacosb Formula,
2 cos A cos B = cos (A + B) + cos (A – B)
= 10 [cos (x + 4x) + cos (x – 4x)]
= 10 [cos 5x + cos (-3x)]
= 10 [cos 5x + cos 3x]
Answer:
Thus, 20 cos x cos 3x in terms of sum function is
10 [cos 5x + cos 3x].
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