Question

Without using trignometric tables, find the value of $\frac{\cos {70}^{\circ }}{\sin {20}^{\circ }}+\cos {57}^{\circ }\text{cosec}{33}^{\circ }-2\cos {60}^{\circ }$.

Answer 1

$\frac{\cos {70}^o}{\sin {20}^o}+\cos {57}^o\cdot cosec{33}^o+2\cos {60}^o$

$=\frac{\cos {70}^o}{\sin ({90}^o-{70}^o)}+\cos ({90}^o-{33}^o)\cdot cosec{33}^o-2\cdot \cos {60}^o$

$=\frac{\cos {70}^o}{\cos {70}^o}+\sin {33}^o\cdot cosec{33}^o-2\cdot \cos {60}^o$

$=1+\frac{1}{cosec{33}^o}\cdot cosec{33}^o-2\times 1/2$

$=1+1-1$

$=1$

$\therefore \frac{\cos {70}^o}{\sin {20}^o}+\cos {57}^o\cdot cosec{33}^o-2\cdot \cos {60}^o=1$.