Question

Find the value of $\frac{\cos {70}^0}{\sin {20}^0}+\cos {57}^0\text{cosec}{33}^0-2\cos {60}^0$

Answer 1

$\frac{{\cos 70}^0}{{\sin 20}^0}+\frac{{\cos 57}^0}{{\sin 33}^0}-2{\cos 60}^0$

$\Rightarrow \frac{\cos (90-20)}{{\sin 20}^0}+\frac{{\cos 57}^0}{\sin 33^0}-2\left(1/2\right)$

$\Rightarrow +\frac{{\sin 20}^0}{{\sin 20}^0}+\frac{\cos (90-{33}^0)}{{\sin 33}^0}-1$

$\Rightarrow \frac{{\sin 33}^0}{{\sin 33}^0}=1$