Question

Find the value of sin^-1⁡(\(\frac{5}{13}\))+cos^-1⁡(\(\frac{3}{5}\)).

(a) sin^-1⁡(\(\frac{63}{65}\))

(b) sin^-1⁡1

(c) 0

(d) sin^-1⁡(\(\frac{64}{65}\))

This question was addressed to me in semester exam.

My query is from Properties of Inverse Trigonometric Functions topic in division Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

The correct option is (a) sin^-1⁡(\(\frac{63}{65}\))

Best explanation: From ∆ABC, we get

cos^-1⁡\((\frac{3}{5})\)=sin^-1⁡\((\frac{4}{5})\)

∴sin^-1⁡(\(\frac{5}{13}\))+cos^-1⁡(\(\frac{3}{5}\))=sin^-1⁡(\(\frac{5}{13}\))+sin^-1⁡(\(\frac{4}{5}\))

=sin^-1⁡\((\frac{5}{13}\sqrt{1-(\frac{4}{5})^2}+\frac{4}{5}\sqrt{1-(\frac{5}{13})^2})\)

=\(sin^{-1}(\frac{5}{13}×\frac{3}{5}+\frac{4}{5}×\frac{12}{13})=sin^{-1}(\frac{15+48}{65})=sin^{-1}(\frac{63}{65})\).