Question

The value of sin(2 tan^–1 (1/3)) + cos (tan^–1 2$\sqrt{2}$) is-

• A. 12/13
• B. 13/14
• C. 14/15
• D. None of these

Answer 1

Answer: (C)

14/15

Answer 2

Let tan^–1 1/3 = a and tan^–1 2$\sqrt{2}$ = b.

Then tan a =1/3 and tan b = 2$\sqrt{2}$, so that

sin (2 tan^–1 (1/3)) + cos (tan^–1 2$\sqrt{2}$)

= sin 2a + cos b

= $\frac{2\tan\alpha}{1 + \tan^{2}\alpha}$+$\frac{1}{\sqrt{1 + \tan^{2}\beta}}$ [Q –p/2 < b < p/2]

= $\frac{2.(1/3)}{1 + (1/9)}$+ $\frac{1}{\sqrt{1 + 8}}$ =$\frac{2}{3}.\frac{9}{10} + \frac{1}{3} = \frac{3}{5} + \frac{1}{3} = \frac{14}{15}$.