Mostre que
Trigonometria: Infinito 11 A - Parte 1 Pág. 99 Ex. 70
Enunciado
Mostre que: $(\cos \alpha -sen\,\alpha )(\cos \alpha +sen\,\alpha )-1=-2\,se{{n}^{2}}\,\alpha $.
Resolução
Ora,
\[\begin{array}{*{35}{l}}
(\cos \alpha -sen\,\alpha )(\cos \alpha +sen\,\alpha )-1 & = & {{\cos }^{2}}\alpha +\cos \alpha \times sen\,\alpha -\cos \alpha \times sen\,\alpha -se{{n}^{2}}\,\alpha -1 \\
{} & = & {{\cos }^{2}}\alpha -se{{n}^{2}}\,\alpha -1 \\
{} & = & -(1-{{\cos }^{2}}\alpha )-se{{n}^{2}}\,\alpha \\
{} & = & -se{{n}^{2}}\,\alpha -se{{n}^{2}}\,\alpha \\
{} & = & -2\,se{{n}^{2}}\,\alpha \\
\end{array}\]
