Question

For the given table choose the correct option
$\begin{array}{cccc}& & & \\ & \text{Column I}& & \text{Column II}\\ \left(a\right)& \text{The value of}\cot \left(\frac{41\pi }{4}\right)\text{is}& \left(p\right)& 1\\ \left(b\right)& \text{The value of}\sec (-{600}^{\circ })\text{is}& \left(q\right)& 2\\ \left(c\right)& \text{The value of}{\text{cosec}}^2\left(\frac{41\pi }{4}\right)\text{is}& \left(r\right)& -2\\ \left(d\right)& \text{The value of}\tan \left(\frac{19\pi }{4}\right)\text{is}& \left(s\right)& -1\end{array}$

• A. $\left(a\right)\to \left(p\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(s\right)$
• B. $\left(a\right)\to \left(p\right),\left(b\right)\to \left(q\right),\left(c\right)\to \left(r\right),\left(d\right)\to \left(s\right)$
• C. $\left(a\right)\to \left(q\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(p\right),\left(d\right)\to \left(s\right)$
• D. $\left(a\right)\to \left(s\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(p\right)$

Answer 1

The correct option is A $\left(a\right)\to \left(p\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(s\right)$

$\left(a\right)\cot \left(\frac{41\pi }{4}\right)=\cot (10\pi +\frac{\pi }{4})$
$=\cot \left(\frac{\pi }{4}\right)=1$

$\left(b\right)$ As we know $2\pi =360°$
$\sec (-{600}^{\circ })=\sec \left(600°\right)$
$=\sec (3\pi +60°)=-\sec \left(60°\right)=-2$

$\left(c\right){\text{cosec}}^2\left(\frac{41\pi }{4}\right)={\text{cosec}}^2(10\pi +\frac{\pi }{4})$
$={\text{cosec}}^2\left(\frac{\pi }{4}\right)=2$

$\left(d\right)\tan \left(\frac{19\pi }{4}\right)=\tan (5\pi -\frac{\pi }{4})=-\tan \frac{\pi }{4}=-1$

$\therefore \left(a\right)\to \left(p\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(s\right)$