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Question: If \(\tan A = \frac{1}{2},\tan B = \frac{1}{3},\) then \(\cos 2A =\)...

If tan⁡A=12,tan⁡B=13,\tan A = \frac{1}{2},\tan B = \frac{1}{3}, then cos⁡2A=\cos 2A =

A

sin⁡B\sin B

B

sin⁡2B\sin 2B

C

sin⁡3B\sin 3B

D

None of these

Answer

sin⁡2B\sin 2B

Explanation

Solution

A+B=45∘,A + B = 45{^\circ},therefore 2A=90∘−2B2A = 90{^\circ} - 2B

∴cos⁡2A=sin⁡2B\therefore\cos 2A = \sin 2B.