January 04 2010
Deriving CosC – CosD = – 2.Sin[(C + D)/2].Sin[(C - D)/2]
This is also one more important mathematical formula in multiple and sub-multiple angles’ trigonometry. We have previously developed summation of sine, summation of cosine and differentiation of sine function with two different angles. Similarly, we are going to derive differentiation of Cosine function.
First of all we have to assume, C and D are different angles of a right angle triangle. Now we are going to subtract these two angles with respect Cosine, which means we are developing simplification of below trigonometric function.
CosC – CosD
It is very complicated or not easy to simplify this trigonometric function directly by using mathematical applications. However, we can simplify this function by taking an assumption. Consider C and D are equal to A + B and A – B respectively for our convenience.