Question

If $\tan\alpha = \frac{1}{7},\mspace{6mu}\tan\beta = \frac{1}{3},$ then $\cos 2\alpha =$

• A. $\sin 2\beta$
• B. $\sin 4\beta$
• C. $\sin 3\beta$
• D. None of these

Answer 1

Answer: (B)

$\sin 4\beta$

Answer 2

$\cos 2\alpha = \frac{1 - t^{2}}{1 + t^{2}} = \frac{24}{25}${Here $t = \tan\alpha$}

$\sin 2\beta = \frac{2T}{1 + T^{2}} = \frac{3}{5} \Rightarrow \cos 2\beta = \frac{4}{5}${$T = \tan\beta$}

$\therefore\sin 4\beta = 2\sin 2\beta\cos 2\beta = 2.\frac{3}{5}.\frac{4}{5} = \frac{24}{25} = \cos 2\alpha$.