The cotangent of the difference of two angles, denoted as cot(a – b), can be expressed using the following formula:
cot(a – b) = \frac{cot a \cdot cot b + 1}{cot b – cot a}
Here’s a breakdown of the terms in the formula:
- cot a: This is the cotangent of angle a, which is defined as the ratio of the adjacent side to the opposite side in a right triangle, or cot a = \frac{1}{tan a}.
- cot b: Similarly, this is the cotangent of angle b.
This formula shows how cotangent behaves when calculating the difference between two angles. It’s important to note that cotangent is the reciprocal of the tangent function; therefore, it can be very useful in trigonometric identities and proofs.
For example, if you have specific angles for a and b, you can plug in their cotangent values into this formula to find the cotangent of the angle a – b. This representation can also be useful in simplifying complex trigonometric expressions or solving trigonometric equations.
In summary, whenever you encounter cotangent differences, remember this formula:
cot(a – b) = \frac{cot a \cdot cot b + 1}{cot b – cot a}