Question

Evaluate: $\frac{\csc {13}^o}{\sec {77}^o}-\frac{\cot {20}^o}{\tan {70}^o}$.

Answer 1

$\frac{\csc {13}^{\circ }}{\sec {77}^{\circ }}-\frac{\cot {20}^{\circ }}{\tan {70}^{\circ }}=\frac{\csc {(90-77)}^{\circ }}{\sec {77}^{\circ }}-\frac{\cot {(90-70)}^{\circ }}{\tan {70}^{\circ }}=\frac{\sec {77}^{\circ }}{\sec {77}^{\circ }}-\frac{\tan {70}^{\circ }}{\tan {70}^{\circ }}=1-1=0$