Question
Download Solution PDFThe value of \(\tan \left(\cos ^{-1} \frac{4}{5}+\tan ^{-1} \frac{2}{3}\right)=\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Given, tan \([cos^{-1}(\frac{4}{5}) + tan^{-1}(\frac{2}{3})]\) = tan \([tan^{-1}(\frac{\sqrt{5^2 - 4^2}}{4}) + tan^{-1}(\frac{2}{3})]\)
= tan \([tan^{-1}(\frac{3}{4}) + tan^{-1}(\frac{2}{3})]\) = tan \([tan^{-1}(\frac{\frac{3}{4} + \frac{2}{3}}{1 - \frac{3 \times 2}{4 \times 3}})]\)
= tan \([tan^{-1}(\frac{9+8}{12-6})]\) = tan \([tan^{-1}(\frac{17}{6})]\) = \(\frac{17}{6}\)
Hence option 4 is correct
Last updated on Jul 3, 2025
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