Question

if sinA+cosA=m and sin³A+cos³A=n,then​

Answer 1

$Answer \: \\ \\ Given \: \: Question \: \: Is \: \: \\ \\ \sin(x) + \cos(x) = m \\ and \\ \sin {}^{3} (x) + \cos {}^{3} (x) = n \\ \\ \\ \sin {}^{3} (x) + \cos {}^{3} (x) = \\ \sin(x) + \cos(x) (( \sin ( x) + \cos(x) ) {}^{2} - 3 \sin(x) \cos(x) ) \\ \\ \\ \sin {}^{3} (x) + \cos {}^{3} (x) = \\ \sin(x) + \cos(x) (1 - \sin(x) \cos(x) ) \\ \\ \\ n = m(1 - m) \\ \\ therefore \: the \: relation \: between \: \: m \: and \: n \: is \: \\ \\ n = m(1 - m) \\ \\ Note \: \\ \\here \: \: \: x = \: a \\ \\ \alpha {}^{3} + \beta {}^{3} = \alpha + \beta (( \alpha + \beta ) {}^{2} - 3 \alpha \beta ) \\ \\ \sin {}^{2} ( x ) + \cos {}^{2} (x) = 1$

Answer 2

Step-by-step explanation:

$\begin{lgathered} \\ \\ \sin(x) + \cos(x) = m \\ \\ and \\ \\ \sin {}^{3} (x) + \cos {}^{3} (x) = n \\ \\ \\ \sin {}^{3} (x) + \cos {}^{3} (x) = \\ \sin(x) + \cos(x) (( \sin ( x) + \cos(x) ) {}^{2} - 3 \sin(x) \cos(x) ) \\ \\ \\ \sin {}^{3} (x) + \cos {}^{3} (x) = \\ \sin(x) + \cos(x) (1 - \sin(x) \cos(x) ) \\ \\ \\ n = m(1 - m) \\ \\ Therefore \: The \: Relation \: Between \: \: m \: and \: n \: Is \: \\ \\ n = m(1 - m) \\ \end{lgathered}$