Question

Simplify the expression

Answer 1

Answer:

  sin(α) -cos(α)

Step-by-step explanation:

$\dfrac{2\sin^2{\alpha}-1}{\sin{\alpha}+\cos{\alpha}}=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{(\sin{\alpha}+\cos{\alpha})(\sin{\alpha}-\cos{\alpha})}\\\\=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{\sin^2{\alpha}-\cos^2{\alpha}}=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{\sin^2{\alpha}-(1-\sin^2{\alpha})}\\\\=\dfrac{(2\sin^2{\alpha}-1)(\sin{\alpha}-\cos{\alpha})}{2\sin^2{\alpha}-1}\\\\=\sin{\alpha}-\cos{\alpha}$