Question

Evaluate the following :
$\frac{2tan{53}^{\circ }}{cot{37}^{\circ }}-\frac{cot{80}^{\circ }}{tan{10}^{\circ }}$

Answer 1

We have,
$\frac{2tan{53}^{\circ }}{cot{37}^{\circ }}-\frac{cot{80}^{\circ }}{tan{10}^{\circ }}=\frac{2tan{53}^{\circ }}{tan({90}^{\circ }-{37}^{\circ })}-\frac{cot({90}^{\circ }-{10}^{\circ })}{tan{10}^{\circ }}=\frac{2tan{53}^{\circ }}{tan{53}^{\circ }}-\frac{tan{10}^{\circ }}{tan{10}^{\circ }}=2-1=1$