Question

please say process for this question very fast

Answer 1

QUESTION :–

$\\ \: {\huge{.}} \bf \: \: If \: \: \sqrt{ \sin(x) } + \cos(x) = 0 \: \: then \: \: \sin(x) = ?$

ANSWER :–

GIVEN :–

$\\ \: \: {\huge{.}} \: \: \bf \sqrt{ \sin(x) } + \cos(x) = 0$

TO FIND :–

$\\ \:\: \sin(x) = ? \:\:$

SOLUTION :–

$\\ \implies \bf \sqrt{ \sin(x) } + \cos(x) = 0$

$\\ \implies \bf \sqrt{ \sin(x) } = - \cos(x)$

• Square on both sides –

$\\ \implies \bf \{\sqrt{ \sin(x) } \} ^{2} = \{ - \cos(x) \}^{2}$

$\\ \implies \bf \sin(x) = \cos^{2} (x)$

• We know that –

$\\ \dashrightarrow \bf \sin ^{2} (x) + \cos^{2} (x) = 1$

• So that –

$\\ \implies \bf \sin(x) =1 - \sin^{2} (x)$

$\\ \implies \bf \sin^{2} (x) + \sin(x) - 1 = 0$

$\\ \implies \bf \sin(x) = \dfrac{ - (1) \pm \sqrt{ {(1)}^{2} - 4(1)( - 1)} }{2}$

$\\ \implies \bf \sin(x) = \dfrac{ - (1) \pm \sqrt{5} }{2}$

$\\ \implies \large{ \boxed{ \bf \sin(x) = \dfrac{ - 1 + \sqrt{5} }{2}}}$

$\\ \rule{220}{2}$