In this article, we will show that sin(A+B)=sinAcosB+cosAsinB.
Let a triangle right angle triangle such that the line AB extend upto a point D. is the hypotenuse of . Let .
Draw a line from AF from A that insect the line CB at E such that
Draw a line from C perpendicular to AF at point G. After that, draw two lines from G, one perpendicular to CB, and another perpendicular to AD.
We can easily show that is similar to and is similar to . Therefore, we can say .
Since, is right angled. Using sin formula, we get
BHGJ is a rectangle. Therefore, . Substituting in above equation,
Substituting equation 2, 3, 4, 5 in equation 1.