Question

$cose{c}^{-1}\left(\frac{3}{2}\right)+co{s}^{-1}\left(\frac{2}{3}\right)-2co{t}^{-1}\left(\frac{1}{7}\right)-co{t}^{-1}\left(7\right)$ is equal to

• A. $co{t}^{-1}7$
• B. $-ta{n}^{-1}7$
• C. $ta{n}^{-1}\left(\frac{1}{7}\right)$
• D. $co{t}^{-1}\left(\frac{1}{7}\right)$

Answer 1

Answer: (B)

$si{n}^{-1}\left(\frac{2}{3}\right)+co{s}^{-1}\left(\frac{2}{3}\right)-ta{n}^{-1}7-co{t}^{-1}7-co{t}^{-1}\left(\frac{1}{7}\right)$
$=\frac{\pi }{2}-\frac{\pi }{2}-co{t}^{-1}\left(\frac{1}{7}\right)=-ta{n}^{-1}7$