1.

What is the value of cos⁡(tan^-1⁡(\(\frac{4}{5}\)))?(a) \(\frac{5}{4}\)(b) \(\frac{5}{\sqrt{41}}\)(c) \(\frac{\sqrt{41}}{5}\)(d) \(\frac{4}{5}\)The question was asked by my college director while I was bunking the class.Origin of the question is Properties of Inverse Trigonometric Functions in portion Inverse Trigonometric Functions of Mathematics – Class 12

Answer» RIGHT choice is (B) \(\frac{5}{\sqrt{41}}\)

EXPLANATION: From ∆ABC, we get

tan^-1⁡(\(\frac{4}{5}\))=cos^-1⁡(\(\frac{5}{\sqrt{41}}\))

cos⁡(tan^-1⁡(\(\frac{4}{5}\))=cos⁡(cos^-1⁡(\(\frac{5}{\sqrt{41}}\)))

=\(\frac{5}{\sqrt{41}}\)


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