Question

Simplify $3\frac{\tan {67}^{\circ }}{\cot {23}^{\circ }}+\frac{1}{2}\frac{\sin {42}^{\circ }}{\cos {48}^{\circ }}+\frac{5}{2}\frac{cosec{61}^{\circ }}{\sec {29}^{\circ }}$

Answer 1

$3\frac{\tan 67°}{\cot 23°}+\frac{1}{2}\frac{\sin 42°}{\cos 48°}+\frac{5}{2}\frac{cosec61°}{\sec 29°}$

$=3\frac{\tan (90°-23°)}{\cot 23°}+\frac{1}{2}\frac{\sin (90°-48°)}{\cos 48°}+\frac{5}{2}\frac{cosec(90°-29°)}{\sec 29°}$

$=3\frac{\cot 23°}{\cot 23°}+\frac{1}{2}\frac{\cos 48°}{\cos 48°}+\frac{5}{2}\frac{\sec 29°}{\sec 29°}$

$=3+\frac{1}{2}+\frac{5}{2}$

$=\frac{6+6}{2}$

$=6.$

Hence, the answer is $6.$