আন্তরিকরণে বিপরীত ত্রিকোণমিতিক অনুপাত

1. \(\frac{d}{dx}(\sin^{-1} x) = \frac{1}{\sqrt{1 - x^2}}\)
2. \(\frac{d}{dx}(\cos^{-1} x) = -\frac{1}{\sqrt{1 - x^2}}\)
3. \(\frac{d}{dx}(\tan^{-1} x) = \frac{1}{1 + x^2}\)
4. \(\frac{d}{dx}(\cot^{-1} x) = -\frac{1}{1 + x^2}\)
5. \(\frac{d}{dx}(\sec^{-1} x) = \frac{1}{x\sqrt{x^2 - 1}}\)
6. \(\frac{d}{dx}(\text{cosec}^{-1} x) = -\frac{1}{x\sqrt{x^2 - 1}}\)

1. \(\sin^{-1}x = \text{cosec}^{-1}\frac{1}{x}\)
2. \(\cot^{-1}x = \tan^{-1}\frac{1}{x}\)

1. \(2\tan^{-1}x = \tan^{-1}\frac{2x}{1 - x^2} = \sin^{-1}\frac{2x}{1 + x^2} = \cos^{-1}\frac{1 - x^2}{1 + x^2}\)
2. \(\tan^{-1}x \pm \tan^{-1}y = \tan^{-1}\frac{x \pm y}{1 \mp xy}\)