Question
Download Solution PDF\(\rm \sin^{-1}\frac{4}{5}-\sin^{-1}\frac{5}{13}=?\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\rm \sin^{-1}\frac{4}{5}-\sin^{-1}\frac{5}{13}\)
Concept:
Use formula
\(\rm sin^{1}x-sin^{-1}y=sin^{-1}[x\sqrt{1-(y)^2}-y\sqrt{1-(x)^2\ }\ ]\)
Calculation:
\(\rm \sin^{-1}\frac{4}{5}-\sin^{-1}\frac{5}{13}\)
\(\rm =sin^{-1}[\frac{4}{5}\sqrt{1-(\frac{5}{13})^2}-\frac{5}{13}\sqrt{1-(\frac{4}{5})^2\ }\ ]\)
\(\rm =sin^{-1}[\frac{48}{65}-\frac{15}{65}]\)
\(\rm =sin^{-1}\frac{33}{65}\)
Hence the option (3) is correct.
Last updated on May 26, 2025
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