If `cos(A-B) = 3/5, tan A*tan B = 2` which of the following is true

Options

A. `sin (A+B)=(1)/(5)`
B. `sin (A+B)=-(1)/(5)`
C. `cos (A-B)=(1)/(5)`
D. `cos (A+B)=-(1)/(5)`

Answer

D

Explanation

Given `tan A tan B=2`
`rArr (sin A sin B)/(cos A cos B)=2`
On applyin componendo and dividendo rule, we get
`( sin A sin B + cos A cos B)/(sin A sin B- cos A cos B) =(2+1)/(2-1)`
`rArr (cos (A-B))/(-cos (A+B))=(3)/(1)`
`rArr (3//5)/(-cos (A+B))=(3)/(1) [ :. cos (A-B)=(3)/(5)]`
`rArr cos (A+B)=-(1)/(5)`