205k views
0 votes
___cosb=1/2[sin(a+b) + sin(a-b)

1 Answer

3 votes
Use the addition and subtraction theorem:

sin (A + B) = sin A + cos B
sin (A - B) = sin A - cos B

From there it's just a matter of simplification.

sin A cos B = 1/2 [ sin (A + B) + sin (A - B) ]
sin A cos B = 1/2 [ sin A cos B + cos A sin B + sin (A - B) ]
sin A cos B = 1/2 [ sin A cos B + cos A sin B + sin A cos B - cos A sin B ]
sin A cos B = 1/2 [ 2 sin A cos B ]
sin A cos B = sin A cos B
User Nawin K Sharma
by
7.7k points

Related questions

asked Dec 12, 2020 111k views
Mejonzhan asked Dec 12, 2020
by Mejonzhan
7.9k points
2 answers
3 votes
111k views