Question

if secA=m+n÷√mn then find sinA
$sec(a ) = m + n \div 2 \sqrt{mn}$

Answer 1

$\sec(a) = \frac{m + n}{ \sqrt{mn} } \\ \cos(a ) = \frac{ \sqrt{mn} }{m + n} \\ \sin(a) = \sqrt{ 1 - { \cos(a) }^{2} } \\ = \sqrt{1 - {( \frac{ \sqrt{mn} }{m + n}) }^{2} } \\ = \sqrt{ \frac{ {(m + n) }^{2} - mn}{ {(m + n)}^{2} } } = \sqrt{ \frac{ {m}^{2} + {n}^{2} + 2mn - mn}{ {(m + n)}^{2} } } \\ = \frac{ \sqrt{ {m}^{2} + {n}^{2} + mn } }{(m + n)}$