Properties with Negative X

Q. $co{t}^{-1}\left(0.2\right)=c,thenfindta{n}^{-1}(-5).$

1. - c
2. 2c
3. $\frac{c}{2}$
4. None of these

Q. $Ifta{n}^{-1}\left(a\right)=\frac{\pi }{4}thenfindta{n}^{-1}(-a).$

1. $\frac{\pi }{4}$
2. $\frac{-\pi }{4}$
3. $\frac{\pi }{3}$
4. $\frac{-\pi }{3}$

Q.

The value of $tan[co{s}^{-1}\left(\frac{-2}{7}\right)-\frac{\pi }{2}]$ is

1. $\frac{2}{3\sqrt{5}}$

2. $\frac{3\sqrt{5}}{2}$

3. $\frac{2}{\sqrt{5}}$

4. None

Q.

Find the number of solutions for the equation $co{s}^{-1}\left(cosx\right)=-\frac{1}{2}$.

1. 1

2. infinite

3. 0

4. 2