Question

Without using trigonometric ratios, evaluate:
$\frac{\cos {58}^0}{\sin {32}^0}+\frac{\sin {22}^0}{\cos {68}^0}-\frac{\cos {38}^0.\text{cosec}{52}^0}{\tan {18}^0.\tan {35}^0.\tan {60}^0.\tan {72}^0.\tan {55}^0}$.

• A. $2-\frac{1}{\sqrt{3}}$
• B. $6-\frac{1}{\sqrt{3}}$
• C. $1$
• D. $0$

Answer 1

The correct option is A $2-\frac{1}{\sqrt{3}}$

$\frac{\cos 58°}{\sin 32°}+\frac{\sin 22°}{\cos 68°}-\frac{\cos 38°.cosec52°}{\tan 18°.\tan 35°.\tan 60°.\tan 72°.\tan 55°}=1+1-\frac{1}{\sqrt{3}}=2-\frac{1}{\sqrt{3}}$