Allied Angles

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

1. $\left(a\right)\to \left(p\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(s\right)$
2. $\left(a\right)\to \left(p\right),\left(b\right)\to \left(q\right),\left(c\right)\to \left(r\right),\left(d\right)\to \left(s\right)$
3. $\left(a\right)\to \left(q\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(p\right),\left(d\right)\to \left(s\right)$
4. $\left(a\right)\to \left(s\right),\left(b\right)\to \left(r\right),\left(c\right)\to \left(q\right),\left(d\right)\to \left(p\right)$

Q. If $\theta =178°$, then the value of $\sin \theta \sqrt{1+{\cot }^2\theta }+\cos \theta \sqrt{1+{\tan }^2\theta }$ is

1. $2$
2. $-2$
3. $0$
4. $1$

Q. The value of $\cot A+\tan (180°+A)+\tan (90°+A)+\tan (360°-A)$ is

Q.

The line OA makes an angle of $\theta ={30}^o$ with negative x-axis as shown in the figure. Which of the following could be the measure of the angle made by OA with respect to positive x-axis?

1. $-{30}^o$

2. $-{150}^o$

3. ${210}^o$

4. ${150}^o$

Q. The arcs of the same length in two circles subtend angles of ${28}^{\circ }$ and ${35}^{\circ }$ at their centres. Then the ratio of their respective radii is

1. $3:4$
2. $4:3$
3. $4:5$
4. $5:4$

Q. The value of ${\sin }^2\frac{\pi }{4}+{\sin }^2\frac{3\pi }{4}+{\sin }^2\frac{5\pi }{4}+{\sin }^2\frac{7\pi }{4}$ is

1. $0$
2. $1$
3. $2$
4. $\frac{1}{2}$

Q. If $\cos A=n\cos B$ and $\sin A=m\sin B$, then $(m^2-n^2){\sin }^{2}B=$

1. $1$
2. $1+n^2$
3. $n^2$
4. $1-n^2$