Properties with Negative X

Q. 17.If secx + tanx = 22/7 and cosecx + cotx = m/n, where m/n is in lowest terms, then the value of (m + n) is equal to (A) 22 (B) 33 (C) 44 (D) 11

Q. The value of $cos\left(\frac{1}{2}co{s}^{-1}\left[cos\right(-\frac{14\pi }{5}\left)\right]\right)$

1. $cos\left(\frac{9\pi }{5}\right)$
2. $sin\left(\frac{-\pi }{5}\right)$
3. $cos\left(\frac{2\pi }{5}\right)$
4. $-cos\left(\frac{3\pi }{5}\right)$

Q. Find the minimum value of the function
$f\left(x\right)=\frac{{\pi }^2}{16{\cot }^{-1}(-x)}-{\cot }^{-1}x.$

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

Q. Prove that: $\cot \frac{\pi }{8}=\sqrt{2}+1$

Q. If $\frac{\pi }{2}<\mathrm{\theta }<\pi ,$ the write the value of $\sqrt{2+\sqrt{2+2\cos 2\mathrm{\theta }}}$ in the simplest form.

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

Q. whats the maximum value of 1/sec theta , 0