Question

cos(alpha+beta)=4/5 and sin ( alpha-beta)=5/13.Find tan 2alpha​

Answer 1

Step-by-step explanation:

1. Take two triangles
2. In 1st triangle mention alpha +beta as angle and find out sin(alpha +beta)
3. In second triangle mention alpha-beta as angle and find out cos (alpha-beta)
4. now you have values of cos(alpha+beta),cos(alpha-beta),sin(alpha+beta)andsin(alpha-beta)
5. now take tan (2alpha) as tan((alpha+beta)+(alpha-beta)) which is in the form of tan(a+b)
6. find values of tan (alpha+beta )and tan(alpha-beta)by dividing the terms in point 4
7. then apply tan((alpha+beta)+(alpha-beta))=((tan(alpha+beta)+tan(alpha-beta))/(1-tan(alpha+beta)*tan(alpha-beta)))