Question

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

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

Answer 1

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

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