Question

Evaluate $\cot \theta \cdot \tan ({90}^o-\theta )-\sec ({90}^o-\theta )\cdot cosec\theta +{\sin }^2{25}^o+{\sin }^2{65}^o+\sqrt{3}\tan 6^o\tan {16}^o\tan {74}^o\tan {84}^o$.

Answer 1

$\cot \theta .\tan ({90}^{\circ }-\theta )-\sec ({90}^{\circ }-\theta ).\csc \theta +{\sin }^2{25}^{\circ }+{\sin }^2{65}^{\circ }+\sqrt{3}\tan 6^{\circ }\tan {16}^{\circ }\tan {74}^{\circ }\tan {84}^{\circ }$

$=-1+1+\left(\sqrt{\times }1\right)$

$=\sqrt{3}$