Question

Simplify the expression

Answer 1

sin(α) -cos(α)

Explanation:

`\frac{2\sin^2{\alpha}-1}{sin(\alpha)+cos(\alpha)}=\frac{(2\sin^2{\alpha}-1)(sin(\alpha)-cos(\alpha))}{(sin(\alpha)+cos(\alpha))(sin(\alpha)-cos(\alpha))}\\\\=\frac{(2\sin^2{\alpha}-1)(sin(\alpha)-cos(\alpha))}{\sin^2{\alpha}-\cos^2{\alpha}}=\frac{(2\sin^2{\alpha}-1)(sin(\alpha)-cos(\alpha))}{\sin^2{\alpha}-(1-\sin^2{\alpha})}\\\\=\frac{(2\sin^2{\alpha}-1)(sin(\alpha)-cos(\alpha))}{2\sin^2{\alpha}-1}\\\\=sin(\alpha)-cos(\alpha)`