Question

Evaluate :
$\frac{\tan {76}^{\circ }}{\cot {14}^{\circ }}+\frac{\sec {58}^{\circ }}{\cos ec{32}^{\circ }}-\sin {35}^{\circ }\sec {55}^{\circ }+8{\sin }^2{30}^{\circ }$

Answer 1

$\left(\frac{tan{76}^o}{cot{14}^o}\right)+\left(\frac{sec{58}^o}{cosec{32}^o}\right)-sin{35}^{o}sec{55}^o+8si{n}^2{30}^o$

$usetan({90}^o-\theta )=cot\theta$

$sec({90}^o-\theta )=cosec\theta$

$sin({90}^o-\theta )=cos\theta$

$\therefore \left(\frac{tan({90}^o-{14}^o)}{cot{14}^o}\right)+\left(\frac{sec({90}^o-{32}^o)}{cosec{32}^o}\right)-sin{35}^{o}sec({90}^o-{35}^o)+8si{n}^2{30}^o$

$=\left(\frac{cot{14}^o}{cot{14}^o}\right)+\left(\frac{cosec{32}^o}{cosec{32}^o}\right)-sin{35}^{o}cosec{35}^o+8(\frac{1}{2}{)}^2$

$=2-1+2$

$=3$