# How do you verify (sinA-cosA)^2=1-2sin^2AcotA?

Nov 12, 2016

see below

#### Explanation:

${\left(\sin A - \cos A\right)}^{2} = 1 - 2 {\sin}^{2} A \cot A$

$\left(\sin A - \cos A\right) \left(\sin A - \cos A\right) = 1 - 2 {\sin}^{2} A \cdot \cos \frac{A}{\sin} A$

${\sin}^{2} A - 2 \sin A \cos A + {\cos}^{2} A = 1 - 2 {\sin}^{\cancel{2}} A \cos \frac{A}{\cancel{\sin}} A$

${\sin}^{2} A + {\cos}^{2} A - 2 \sin A \cos A = 1 - 2 \sin A \cos A$

$1 - 2 \sin A \cos A = 1 - 2 \sin A \cos A$

$\therefore$Left Hand Side = Right Hand Side