Question

Evaluate the following :
$\frac{2cos{67}^{\circ }}{sin{23}^{\circ }}-\frac{tan{40}^{\circ }}{cot{50}^{\circ }}-cos{0}^{\circ }$

Answer 1

$\frac{2cos{67}^{\circ }}{sin{23}^{\circ }}-\frac{tan{40}^{\circ }}{cot{50}^{\circ }}-cos{0}^{\circ }$

$=\frac{2cos({90}^{\circ }-{23}^{\circ })}{sin{23}^{\circ }}-\frac{tan({90}^{\circ }-{50}^{\circ })}{cot{50}^{\circ }}-cos{0}^{\circ }$

$=\frac{2sin{23}^{\circ }}{sin{23}^{\circ }}-\frac{cot{50}^{\circ }}{cot{50}^{\circ }}-cos{0}^{\circ }$ $[\because cos({90}^{\circ }-\theta )=sin\theta andtan({90}^{\circ }-\theta )=cot\theta ]$

= 2 $\times$ 1 - 1 - 1 = 0 $[\because cos{0}^{\circ }=1]$