Prove that sin - 14-5 - sin - 17-25 - sin - 1117-125

sin^ 145+sin^ 1725=sin^ 1117125 sin^ 1A+sin^ 1B=sin^ 1(A√(1 B^2)+B√(1 A^2)) =sin^ 1(45√(1 49625)+725√(1 1625)) =sin^ 1(45√(576625)+725√(925) ...

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Values of Trigonometric Ratios

Prove that ...

Question

Prove that ${sin}^{- 1} \frac{4}{5} + {sin}^{- 1} \frac{7}{25} = {sin}^{- 1} \frac{117}{125}$

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{sin}^{- 1} \frac{4}{5} + {sin}^{- 1} \frac{5}{13} + {sin}^{- 1} (\frac{16}{65}) = \frac{π}{2}

{sin}^{- 1} \frac{3}{5} + {sin}^{- 1} \frac{8}{17} = {sin}^{- 1} \frac{77}{85}

{sin}^{- 1} (117 / 125)

{sin}^{- 1} \frac{5}{13} + {sin}^{- 1} \frac{7}{25} = {cos}^{- 1} \frac{253}{325}

Prove that $s i n^{- 1} \frac{8}{17} + s i n^{- 1} \frac{3}{5} = s i n^{- 1} \frac{77}{85} .$

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