Question

Solve:$|\frac{\sin 50}{\cos 40}+\frac{\csc 40}{\sec 50}-4\cos 50x\csc 40|$.

Answer 1

$|\frac{\sin {50}^{\circ }}{\sin {40}^{\circ }}+\frac{\cos ec{40}^{\circ }}{\sec {50}^{\circ }}-4\cos {50}^{\circ }\cos ec{40}^{\circ }|$

$=|\frac{\sin {50}^{\circ }}{\sin ({90}^{\circ }-{40}^{\circ })}+\frac{\cos ec{40}^{\circ }}{co\sec ({90}^{\circ }-{50}^{\circ })}-4\cos {50}^{\circ }sec({90}^{\circ }-{40}^{\circ })|$

$=|\frac{\sin {50}^{\circ }}{\sin {50}^{\circ }}+\frac{\cos ec{40}^{\circ }}{co\sec {40}^{\circ }}-4\cos {50}^{\circ }sec{50}^{\circ }|$

$=|1+1-4\times 1|$

$=|2-4|$

$=|-2|$ =$2$