*For Suitable values of domain, we have*

*\tan ^{-1} A+\tan ^{-1} B=\tan ^{-1} \left(\frac{A+B}{1-AB} \right) *

* \tan ^{-1} A-\tan ^{-1} B=\tan ^{-1} \left(\frac{A-B}{1+AB} \right) *

* sin^{-1}\theta + cos^{-1}\theta = \frac{\pi}{2} *

* tan^{-1}\theta + cot^{-1}\theta = \frac{\pi}{2} *

* sec^{-1}\theta + cosec^{-1}\theta = \frac{\pi}{2} *

* sin^{-1}(-\theta)= -sin^{-1 }\theta *

* tan^{-1}(-\theta)= -tan^{-1 }\theta *

* cosec^{-1}(-\theta)= -cosec^{-1 }\theta *

* cos^{-1}(-\theta)= \pi - cos^{-1 }\theta *

* sec^{-1}(-\theta)= \pi - sec^{-1 }\theta *

* cot^{-1}(-\theta)= \pi - cot^{-1 }\theta *

* sin^{-1}\theta = cosec^{-1}{\frac{1}{\theta}}*

* cosec^{-1}\theta = sin^{-1}{\frac{1}{\theta}}*

* cos^{-1}\theta = sec^{-1}{\frac{1}{\theta}}*

* sec^{-1}\theta = cos^{-1}{\frac{1}{\theta}}*

* tan^{-1}\theta = cot^{-1}{\frac{1}{\theta}}*

* cot^{-1}\theta = tan^{-1}{\frac{1}{\theta}}*

*2\tan ^{-1} \theta =\sin ^{-1} \left(\frac{2\theta }{1+\theta ^{2} } \right)\, \, =\, \, \cos ^{-1} \left(\frac{1-\theta ^{2} }{1+\theta ^{2} } \right)\, \, \, =\, \, \tan ^{-1} \left(\frac{2\theta }{1-\theta ^{2} } \right)*