Question
$\text{Prove that:} \sin^{-1} \bigg(\frac{4}{5}\bigg) + \sin^{-1} \bigg(\frac{5}{13}\bigg) + \sin^{-1} \bigg(\frac{16}{65}\bigg) = \frac{\pi}{2}$
$\text{LHS} = \tan^{-1} \Big(\frac{4}{3}\Big) + \tan^{-1}\Big(\frac{5}{12}\Big) + \tan^{-1} \Big(\frac{16}{63}\Big) = \tan^{-1} \Bigg (\frac{\frac{4}{3} + \frac{5}{12}}{1 - \frac{4}{3}. \frac{5}{12}}\Bigg) + \tan^{-1} \Big(\frac{16}{63}\Big)$
$= \tan^{-1} \bigg(\frac{63}{16}\bigg) + \cot^{-1} \bigg(\frac{63}{16}\bigg)$
$=\frac{\pi}{2}$
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
f : R → R, defined by f(x) = 1 + x2