If A =1 2 , B=1 3 , then 2 A= - Vidyadip

MCQ

If $\tan A =\frac{1}{2}, \tan B=\frac{1}{3}$, then $\cos 2 A=$

A
sin B
✓
sin 2B
C
sin 3B
D
- sin 2B

✓

Answer

Correct option: B.

sin 2B

(B)
$\tan (A+B)=\frac{\frac{1}{2}+\frac{1}{3}}{1-\frac{1}{2} \cdot \frac{1}{3}}=1$
$\therefore \quad A + B =45^{\circ}$
$\Rightarrow 2 A=90^{\circ}-2 B$
$\Rightarrow \cos 2 A=\sin 2 B$
$\ldots\left[\because \cos \left(90^{\circ}-\theta\right)=\sin \theta\right]$

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