Question

Calcule o valor da expressão y= (cosx + senx) . (sex - cosx)

Answer 1

$\textrm{Produto not\'avel:}\\ \mathrm{(a+b)(a-b)=a^2-b^2}\\\\ \mathrm{y=(\sin{x}+\cos{x})(\sin{x}-\cos{x})}\\ \mathrm{y=\sin^2{x}-\cos^2{x}\ \to\ y=-(\cos^2{x}-\sin^2{x})}\\\\ \textrm{Identidade trigonom\'etrica:}\\ \mathrm{\cos{2x}=\cos^2{x}-\sin^2{x}}\\\\ \mathbf{y=-\cos{2x}}$