Question

Evaluate :

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

Answer 1

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

$=3\cos ({90}^{\circ }–{10}^{\circ })cosec{10}^{\circ }+2\sin ({90}^{\circ }–{31}^{\circ })\sec {31}^{\circ }$

$=3\sin {10}^{\circ }cosec{10}^{\circ }+2\cos {31}^{\circ }\sec {31}^{\circ }$

$=3\left(1\right)+2\left(1\right)$

$=3+2$

$=5$