Question

\( \frac{-\tan \theta \cot (90-\theta)+\sec \theta \operatorname{cosec} \theta(90-\theta)+\sin ^{2} 35^{\circ}+\sin ^{2} 55^{\circ}}{\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 70^{\circ} \tan 80^{\circ}} \) (a) \( 2 \sqrt{3} \) (b) \( 2 \sqrt{2} \) (c) \( 3 \sqrt{3} \) (d) \( 4 \sqrt{3} \)

Answer 1

{(cosθ-sinθ)(1+sinθ)+sin²35°+sin²5°}✓3/cosθ.sinθ

Answer 2

\(\frac{-\tan \theta \cot (90-\theta)+\sec \theta \operatorname{cosec} \theta(90-\theta)+\sin ^{2} 35^{\circ}+\sin ^{2} 55^{\circ}}{\tan 10^{\circ} \tan 20^{\circ} \tan 30^{\circ} \tan 70^{\circ} \tan 80^{\circ}}\)

\(=\) \(\frac{-tanθ. tanθ + secθ.secθ + sin^235° + cos^235°}{tan 10° tan 20° tan 30° cot 20° cot 10°} \)

\(=\) \(\frac{sec^2θ - tan^2θ + 1}{\frac{1}{√3} } \)

\(=\)\(\frac{1 + 1}{\frac{1}{√3} } \)

\(=\) 2\(\sqrt{3} \)

Option (a) is correct.