Question

Show that
$\mathtt{ {sin}^{ - 1} \frac{3}{5} } = x \: and \: {sin}^{ - 1 } \frac{8}{17} = y$
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Answer 1

$\underline{\huge{Answer:-}}$

Explanation:

Let $\mathtt{ {sin}^{ - 1} \frac{3}{5} } = x \: and \: {sin}^{ - 1 } \frac{8}{17} = y$

$\implies \large \mathbb{sin \: x = \frac{3}{5} \: and \: sin \: y = \frac{8}{17} }$

$\implies \: \large \mathbb{cos \: x = \sqrt{1 - {sin}^{2} \: x } = \sqrt{1 - \frac{9}{25} } = \frac{4}{5} }$

$\implies \: \large \mathbb{cos \: y = \sqrt{1 - {sin}^{2} \: y} = \sqrt{1 - \frac{64}{289} } = \frac{15}{17} }$

$\implies \: \large \mathbb{ \cos(x - y) = cos \: x \: cos \: y + sin \: x \: sin \: y}$

$\implies \: \large \mathbb{ = \frac{4}{5} \times \frac{15}{17} + \frac{3}{5} \times \frac{8}{17} = \frac{84}{85} }$

$\implies \: \large \mathbb{x - y = {cos}^{ - 1}( \frac{84}{85} )}$

$\large \fbox \mathtt{Hence \: \: \: {sin}^{ - 1} \frac{3}{5} - {sin}^{ - 1} \frac{8}{17} = {cos}^{ - 1} \frac{84}{85} }$

Answer 2

Answer:

5×7-4×6

5×7-4×6=35-24

5×7-4×6=35-24=11

Hope it helps you!