Question

$\frac{\cos 40°}{\sin 50°}+\frac{\sec 40°}{\mathrm{cosec}50°}-2\cos 50°\mathrm{cosec}40°$

Answer 1

Find the value of given expression

$\frac{\cos 40°}{\sin 50°}+\frac{\sec 40°}{\mathrm{cosec}50°}-2\cos 50°\mathrm{cosec}40°$

$=\frac{\cos 40°}{\sin (90°-40°)}+\frac{\sec 40°}{\mathrm{cosec}(90°-40°)}-2\cos 50°\mathrm{cosec}(90°-50°)$

$=\frac{\cos 40°}{\cos 40°}+\frac{\sec 40°}{\sec 40°}-2\cos 50°\sec 50°$

$=1+1-2\cos 50°\times \frac{1}{\cos 50°}$

$=1+1-2$

$=2-2$

$=0$