Question

If cos (A-B) = $\frac{3}{5}$ and tanAtanB = 2,then

• A. cosA cos B =
• B. sinA sin B =
• C. cos (A+B) =
• D. sinAcos B =

Answer 1

The correct option is C

cos (A+B) =

We are given two conditions. Cos(A-B) = $\frac{3}{5}$ or

cosAcosB+sinAsinB = $\frac{3}{5}$ _____ (1)

and

tanAtanB = 2 or

sinAsinB = 2cosAcosB ______(2)
from (1) and (2) , we have cosAcosB + 2cosAcosB = $\frac{3}{5}$
$\Rightarrow$ cosAcosB=$\frac{1}{5}$ and sinAsinB=$\frac{2}{5}$
$\therefore$ cos (A+B) = $\frac{-1}{5}$