Question

Evaluate : $\frac{sec\theta cosec({90}^{\circ }-\theta )-tan\theta cot({90}^{\circ }-\theta )+si{n}^2{55}^{\circ }+si{n}^2{35}^{\circ }}{tan{10}^{\circ }tan{20}^{\circ }tan{60}^{\circ }tan{70}^{\circ }tan{80}^{\circ }}$

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

Answer 1

The correct option is B $\frac{2}{\sqrt{3}}$

$\frac{\sec \theta \csc (90-\theta )-\tan \theta \cot (90-\theta )+{\sin }^{2}55+{\sin }^{2}35}{\tan 10\tan 20\tan 60\tan 70\tan 80}$

$=\frac{(\sec \theta \times \sec \theta )-(\tan \theta \times \tan \theta )+{\sin }^{2}55+{\cos }^{2}55}{\tan 10\frac{1}{\tan 10}\tan 20\frac{1}{\tan 20}\tan 60}$

$=\frac{({\sec }^2\theta -{\tan }^2\theta )+{\sin }^{2}55+{\cos }^{2}55}{\tan 60}$

$=\frac{1+1}{\sqrt{3}}$

$=\frac{2}{\sqrt{3}}$