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Subjects

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

What is the correct value of \(\tan(\sin^{-1}x)\)?What is the correct value of \(\sin(\tan^{-1}x)\)?What is the correct value of \(\cos(\tan^{-1}x)\)?What is the value of \(\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)+\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)\)?If \(\theta=\sin^{-1}\left(\frac{3}{5}\right)\), what is the value of \(\cos\theta\)?If \(\theta=\tan^{-1}\left(\frac{5}{12}\right)\), what is \(\sin\theta\)?When is (\cos^{-1}x=\frac{\pi}{2}-\sin^{-1}x) true?What type of function is f(x)=\cos^{-1}x on its domain \([-1,1]\)?Which statement is correct for \(\tan^{-1}x=\sin^{-1}\left(\frac{x}{\sqrt{1+x^2}}\right)\)?What is the value of \(\sin\left(\cos^{-1}\left(\frac{7}{25}\right)\right)\)?What is the correct value of \(\tan\left(\cos^{-1}x\right)\), when \(0<x<1\)?