Question

Find the value of ${\sec }^2\frac{5\pi }{6}+cosec\frac{7\pi }{6}-\cot \frac{3\pi }{4}$.

Answer 1

${\sec }^2\frac{5\pi }{6}+\csc \left(\frac{7\pi }{6}\right)-\cot \left(\frac{3\pi }{4}\right)$

$={\sec }^2(\pi -\frac{\pi }{6})+\csc (\pi +\frac{\pi }{6})-\cot (\pi -\frac{\pi }{4})$

$={\sec }^2\frac{\pi }{6}-\csc \frac{\pi }{6}+\cot \frac{\pi }{4}$

$=\frac{4}{3}-2+0$

$=\frac{4-6}{3}$

$=\frac{-2}{3}$

Hence, solved.