$\quad \sin x + \cos x = m$
$\Rightarrow (\sin x +\cos x)^2 = m^2$
$\Rightarrow 1 + 2\sin x\cos x = m^2$
$\Rightarrow \sin x\cos x =\dfrac{m^2 -1}{2}$
Ta được:
$+)\quad A = \sin^3x +\cos^3x$
$\to A = (\sin x +\cos x)^3 - 3\sin x\cos x(\sin x + \cos x)$
$\to A = m^3 - 3\cdot \dfrac{m^2 - 1}{2}\cdot m$
$\to A = \dfrac{3m - m^3}{2}$
$+)\quad B = \sin^4x +\cos^4x$
$\to B = (\sin^2x + \cos^2x)^2 - 2\sin^2x\cos^2x$
$\to B = 1 - 2\cdot \left(\dfrac{m^2 -1}{2}\right)^2$
$\to B = \dfrac{3 - m^2}{2}$
