Question

Without using tables evaluate $3\cos {80}^o.\text{cosec}{10}^o+2\sin {59}^o.\sec {31}^o$.

Answer 1

$3\cos {80}^{\circ }.\text{cosec}{10}^{\circ }+2\sin {59}^{\circ }.\sec {31}^{\circ }$

$=3\cos {80}^{\circ }\text{cosec}({90}^{\circ }-{80}^{\circ })+2\sin {59}^{\circ }sec({90}^{\circ }-{59}^{\circ })$

$=3\cos {80}^{\circ }\sec {80}^{\circ }+2\sin {59}^{\circ }\text{cosec}{59}^{\circ }$

$=3\cos {80}^{\circ }\times \frac{1}{\cos {80}^{\circ }}+2\sin {59}^{\circ }\times \frac{1}{\sin {59}^{\circ }}$

$=3+2=5$.