If (A-B)=3 5 and A B=2, then - Vidyadip

MCQ

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

✓
$\cos A \ \cos B =\frac{1}{5}$
B
$\sin A \ \sin B=-\frac{2}{5}$
C
$\cos A \ \cos B =-\frac{1}{5}$
D
$\sin A \ \sin B=-\frac{1}{5}$

✓

Answer

Correct option: A.

$\cos A \ \cos B =\frac{1}{5}$

(A)
Given, $\cos ( A - B )-\frac{3}{5}$
$\therefore 5 \cos A \cos B+5 \sin A \sin B=3 \quad\ldots(i)$
Also, $\tan A \tan B =2$
$\therefore \sin A \sin B=2 \cos A \cos B \quad\ldots(ii)$
From (i) and (ii), we get
$\cos A \cos B =\frac{1}{5}$ and $\sin A \sin B =\frac{2}{5}$

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