Question

please simplify. it is very urgent ​

Answer 1

★★ Heya ★★

a³ + b³ = ( a + b )³ - 3ab ( a + b )

=>

$( \sin( \alpha ) + \cos( \alpha ) ) {}^{3} - 3 \sin( \alpha ) \times \cos( \alpha ) \times ( \sin( \alpha ) + \cos( \alpha ) ) \\ - - - - - - - - - - - - - - - - - - - - - - - - - - \: \: \: + ( \sin( \alpha ) \times \cos( \alpha ) ) \\ ( \sin( \alpha ) + \cos( \alpha ) ) \\ \\ \\ \sin( \alpha ) + \cos( \alpha ) (( \sin( \alpha ) + \cos( \alpha ) ) {}^{2} ) - 3 \sin( \alpha ) \times \cos( \alpha ) \\ - - - - - - - - - - - - - - - - - - - - - - - - + \: \: \: \sin( \alpha ) \times \cos( \alpha ) \\ ( \sin( \alpha ) + \cos( \alpha ) ) \\ \\ \\( 1 - \sin( \alpha ) \times \cos( \alpha ) ) + (\cos( \alpha ) \times \sin( \alpha ) ) \\ \\ \\ = 1$