Question

Find the value of ${\left(\frac{3\cos {43}^{\circ }}{\sin {47}^{\circ }}\right)}^2-\frac{\cos {37}^{\circ }.\text{cosec}{53}^{\circ }}{\tan 5^{\circ }.\tan {25}^{\circ }.\tan {45}^{\circ }.\tan {65}^{\circ }\tan {85}^{\circ }}$

• A. $7$
• B. $0$
• C. $1$
• D. $8$

Answer 1

The correct option is D $8$

${\left(\frac{3\cos {43}^{\circ }}{\sin {47}^{\circ }}\right)}^2-\frac{\cos {37}^{\circ }.\text{cosec}{53}^{\circ }}{\tan 5^{\circ }.\tan {25}^{\circ }.\tan {45}^{\circ }.\tan {65}^{\circ }\tan {85}^{\circ }}=?$

$={\left(\frac{3\cos {43}^{\circ }}{\sin {47}^{\circ }}\right)}^2-\frac{\cos {37}^{\circ }\times \text{cosec}{53}^{\circ }}{\tan 5^{\circ }\times \tan {25}^{\circ }\times \tan {45}^{\circ }\times \tan {65}^{\circ }\times \tan {85}^{\circ }}$

$={\left(\frac{3\sin {47}^{\circ }}{\sin {47}^{\circ }}\right)}^2-\frac{\cos {37}^{\circ }}{\sin {53}^{\circ }}\times \frac{1}{\tan 5^{\circ }\times \tan {25}^{\circ }\times \left(1\right)\times cot{25}^{\circ }\times cot{5}^{\circ }}$

$=3^2-\frac{\sin {53}^{\circ }}{\sin {53}^{\circ }}\times \frac{1}{\frac{\tan 5^{\circ }}{\tan 5^{\circ }}\times \frac{\tan {25}^{\circ }}{\tan {25}^{\circ }}}$

$=9-1=8$

Hence, option 'D' is correct.