Question

The value of 2$\times 2{\sin }^2\frac{\pi }{6}+2{\text{cosec}}^2\frac{7\pi }{6}{\cos }^2\frac{\pi }{3}$

Answer 1

$2\times 2{\sin }^2\frac{\pi }{6}+2cose{c}^2\frac{7\pi }{6}{\cos }^2\frac{\pi }{3}$

$=2\times 2{\left(\frac{1}{2}\right)}^2+2\times cose{c}^2(\pi +\frac{\pi }{6}){\left(\frac{1}{2}\right)}^2$

$=1+2\times {[-cosec\left(\frac{\pi }{6}\right)]}^2\times \frac{1}{4}$

$=1+{(-2)}^2\times \frac{1}{2}$

$=1+2=3$