Question

The value of the expression $\sec 610^{\circ} \operatorname{cosec} 160^{\circ}-\cot 380^{\circ} \tan 470^{\circ}$ is equal to

• A. $\cos ^{-1}(\cos (-1))$
• B. $\cot \left(\cot ^{-1}(-1)\right)$
• C. The gradient of the tangent to the curve $x y=1$ at its point with abscissa 1 .
• D. The greatest integer satisfying the inequality $\frac{2 x+1}{3}-\frac{3 x-1}{2}>1$.

Answer 1

Answer: (B), (C), (D)

$\sec \left(720^{\circ}-110^{\circ}\right) \operatorname{cosec}\left(180^{\circ}-20^{\circ}\right)-\cot \left(360^{\circ}+20^{\circ}\right) \tan \left(360^{\circ}+110^{\circ}\right)$
$=\frac{1}{\cos 110^{\circ}} \cdot \frac{1}{\sin 20^{\circ}}-\cot 20^{\circ} \tan 110^{\circ} $
$=\frac{-1}{\sin ^2 20^{\circ}}+\cot ^2 20^{\circ}=-\left[\operatorname{cosec}^2 20^{\circ}-\cot ^2 20^{\circ}\right]=-1$
$\text { Now verify B, C, D }$