Question

$co{s}^{-1}(-\frac{1}{2})-2si{n}^{-1}\left(\frac{1}{2}\right)+3co{s}^{-1}(-\frac{1}{\sqrt{2}})-4ta{n}^{-1}(-1)$ equals to

• A. 19π/12
• B. 35π/12
• C. 47π/12
• D. 43π/12

Answer 1

The correct option is D

43π/12

$co{s}^{-1}(-\frac{1}{2})-2si{n}^{-1}\left(\frac{1}{2}\right)+3co{s}^{-1}(-\frac{1}{\sqrt{2}})-4ta{n}^{-1}(-1)$
$=co{s}^{-1}\left(cos\frac{2\pi }{3}\right)-2si{n}^{-1}\left(sin\frac{\pi }{6}\right)+3co{s}^{-1}\left(cos\frac{3\pi }{4}\right)-4ta{n}^{-1}tan(-\frac{\pi }{4})$
$=\frac{2\pi }{3}-2.\frac{\pi }{6}+3.\frac{3\pi }{4}+4.\frac{\pi }{4}$
$=\frac{2\pi }{3}-\frac{\pi }{3}+\frac{9\pi }{4}+\pi$
$=\frac{8\pi -4\pi +27\pi +12\pi }{12}=\frac{43\pi }{12}$