As we know that there are six Trigonometric functions of angles and their names are:
- Sine
- Cosine
- Tangent
- Cotangent
- Secant
- Cosecant
These functions are in relation to the right triangle in the following way:
In any right triangle ABC,
| Sin A = Perpendicular/ Hypotenuse |
| Cos A = Base/ Hypotenuse |
| Tan A = Perpendicular/ Base |
| Cot A = Base/ Perpendicular |
| Cosec A = Hypotenuse/Perpendicular |
| Sec A = Hypotenuse/ Base |
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
Example 1: Prove that
Solution:
Using the formula 2 cos A cos B = cos (A + B) + cos (A – B),
Using the formula of cos x – cos y,
Hence, proved that
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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