$$ \text { Evaluate: } \cot ^{-1}\left(-\frac{3}{\sqrt{3}}\right)-\sec ^{-1}\left(-\frac{2}{\sqrt{2}}\right)-\operatorname{cosec}^{-1}(-1)-\tan ^{-1}(1) $$

$$ \text { The function } f(x)=\tan ^{-1}(\sin x+\cos x) \text { is an increasing function in } $$

$$ \text { Evaluate: } \cos ^{-1}\left(\cos \frac{35 \pi}{18}\right)-\sin ^{-1}\left(\sin \frac{35 \pi}{18}\right) $$

Evaluate :

$$ \operatorname{cosec}^{-1}\left(-\frac{2 \sqrt{3}}{3}\right)+\tan ^{-1}\left(-\frac{\sqrt{3}}{3}\right)+\sec ^{-1} 2+\cos ^{-1}\left(-\frac{1}{2}\right)-\sin ^{-1}\left(\frac{\sqrt{2}}{2}\right)$$