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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.
Medium · Level 2 · 2 questions
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\(\frac{24}{25}\)
\(\frac{7}{25}\)
-\(\frac{24}{25}\)
\(\frac{25}{24}\)
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\(\frac{\sqrt{1-x^2}}{x}\)
\(\frac{x}{\sqrt{1-x^2}}\)
\(\sqrt{1+x^2}\)
-\(\frac{\sqrt{1-x^2}}{x}\)
Question 1MediumLevel 2
What is the value of \(\sin\left(\cos^{-1}\left(\frac{7}{25}\right)\right)\)?\(\sin\left(\cos^{-1}\left(\frac{7}{25}\right)\right)\) का मान क्या है?
Correct answer:सही उत्तर:A
Taking \(\theta=\cos^{-1}\left(\frac{7}{25}\right)\), we have \(\theta\in[0,\pi]\) and \(sin\theta\ge0\). Hence from the (7,24,25) triangle, \(\sin\theta=\frac{24}{25}\).\(\theta=\cos^{-1}\left(\frac{7}{25}\right)\) लेने पर \(\theta\in[0,\pi]\) और \(sin\theta\ge0\)। इसलिए (7,24,25) triangle से \(\sin\theta=\frac{24}{25}\)।
What is the correct value of \(\tan\left(\cos^{-1}x\right)\), when \(0<x<1\)?\(\tan\left(\cos^{-1}x\right)\) का सही मान क्या है, जब \(0<x<1\)?
Correct answer:सही उत्तर:A
If \(\theta=\cos^{-1}x\), then \(\cos\theta=x\) and \(\sin\theta=\sqrt{1-x^2}\). Hence \(\tan\theta=\frac{\sqrt{1-x^2}}{x}\).यदि \(\theta=\cos^{-1}x\), तो \(\cos\theta=x\) और \(\sin\theta=\sqrt{1-x^2}\)। इसलिए \(\tan\theta=\frac{\sqrt{1-x^2}}{x}\)।
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