Question

If we consider only the principal values of the
inverse trigonometric functions, then the value of
$tan(co{s}^{-1}\frac{1}{5\sqrt{2}}-si{n}^{-1}\frac{4}{\sqrt{17}})$ is

• A. $\sqrt{\frac{29}{3}}$
• B. $\frac{29}{3}$
• C. $\sqrt{\frac{3}{29}}$
• D. $\frac{3}{29}$

Answer 1

The correct option is D $\frac{3}{29}$

$tan(co{s}^{-1}\frac{1}{5\sqrt{2}}-si{n}^{-1}\frac{4}{\sqrt{17}})$
$tan(ta{n}^{-1}7-ta{n}^{-1}4)$

$=\frac{tanta{n}^{-1}7-tanta{n}^{-1}4}{1+\left(tanta{n}^{-1}7\right)\left(tanta{n}^{-1}4\right)}$
$=\frac{7-4}{1+28}=\frac{3}{29}$