Mathematics
Properties of inverse trigonometric functions
प्रतिलोम त्रिकोणमितीय फलनों के गुणधर्म
In Class 12 Mathematics, this topic from the chapter “Inverse Trigonometric Functions” helps students understand the principal values, domains, and ranges of sin⁻¹x, cos⁻¹x, tan⁻¹x and related functions. It covers standard identities, relationships between inverse trigonometric functions, and the conditions needed to simplify expressions correctly. Students also learn to evaluate compositions and use these properties to solve equations and verify results without confusing restricted angles or function branches.
Practice questions
If \(x\in[-1,1]\), what is the value of \(\sin(\sin^{-1}x)\)?If \(x\in[-1,1]\), what is the value of \(\cos(\cos^{-1}x)\)?What is the value of \(\tan(\tan^{-1}x)\)?In which interval does the principal value of \(\tan^{-1}x\) lie?What is the value of \(sin^{-1}\left(\frac{3}{5}\right)+\cos^{-1}\left(\frac{3}{5}\right)\)?Find the value of \(\cos^{-1}\left(\frac{4}{5}\right)+\sin^{-1}\left(\frac{4}{5}\right)\).What is the value of \(tan^{-1}x+\tan^{-1}\left(\frac{1}{x}\right)\) when \(x>0\)?What is the value of \(tan^{-1}2+\tan^{-1}\left(\frac{1}{2}\right)\)?What is the value of \(tan^{-1}\left(-3\right)+\cot^{-1}\left(-3\right)\)?What is \(\sin^{-1}(-x)\) equal to for \(x\in[-1,1]\)?What is the correct form of \(\tan^{-1}(-x)\)?If \(\theta=\tan^{-1}\left(\frac{3}{4}\right)\), what is the value of \(\sin\theta\)?What is the value of \(\sin\left(\cos^{-1}x\right)\) when \(x\in\left[-1,1\right]\)?What is the value of \(\cos\left(\sin^{-1}x\right)\) when \(x\in\left[-1,1\right]\)?What is the value of \(\tan\left(\sin^{-1}\left(\frac{3}{5}\right)\right)\)?What is the value of \(\cot\left(\cos^{-1}\left(\frac{5}{13}\right)\right)\)?If \(\theta=\tan^{-1}\left(\frac{7}{24}\right)\), what is the value of \(\sec\left(\tan^{-1}\left(\frac{7}{24}\right)\right)\)?What is the value of \(cosec\left(\cos^{-1}\left(\frac{8}{17}\right)\right)\)?What is the value of \(\sin^{-1}\left(\cos\frac{\pi}{3}\right)\)?What is the value of \(\cos^{-1}\left(\sin\frac{\pi}{6}\right)\)?