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(i) Write the principal value of sin−1(\(\frac{1}{2}\))

(ii) Show that

sin -1 (\(\frac{3}{5}\)) - sin-1 \(\frac{8}{17}\) = cos-1 \(\frac{84}{85}\)

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ago by (18.5k points)
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(i) sin-1 \((\frac{1}{2})\) = \(\frac{π}{6}\)

(ii) Let sin-1 (\(\frac{3}{5}\)) = x and sin-1 (\(\frac{8}{17}\)) = y

sin x = \(\frac{3}{5}\) ⇒ cos x = \(\sqrt{1-sin^2x}\)

\(\sqrt{1- (\frac {3}{5})^2}\) = \(\frac{4}{5}\) ; sin y = \(\frac{8}{17}\)

cos (x - y) = cos x cos y + sin x sin y

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