Question

$co{s}^{-1}x\{-cos\left(\frac{-13\pi }{6}\right)\}$ is equal to

• A. $-\frac{\pi }{6}$
  
• B. $\frac{5\pi }{6}$
  
• C. $\frac{\pi }{6}$
  
• D. None

Answer 1

The correct option is B

$\frac{5\pi }{6}$

$co{s}^{-1}x\{-cos\left(\frac{-13\pi }{6}\right)\}Usetheresultco{s}^{-1}(-x)=\pi -co{s}^{-1}x=\pi -co{s}^{-1}\left(cos\left(\frac{13\pi }{6}\right)\right)=\pi -co{s}^{-1}\left(cos(2\pi +\frac{\pi }{6})\right)=\pi -co{s}^{-1}\left(cos\left(\frac{\pi }{6}\right)\right)=\pi -\frac{\pi }{6}=\frac{5\pi }{6}$