LHS
\begin{equation*}
\begin{split}
& (\sin x + \cos x)^2 - 2 \tan x \cos^2 x \quad {\color {blue} (a + b)^2 = a^2 + 2ab + b^2}\\\\
& \sin^2 x + 2 \sin x \cos x + \cos^2 x - 2 \:.\: \frac{\sin x}{\cancel {\cos x}} \:.\: \cancel {\cos^2 x} \\\\
& 1 + \cancel {2 \sin x \cos x} - \cancel {2 \sin x \cos x} \\\\
& 1 \ce{->} \textbf{RHS}
\end{split}
\end{equation*}
LHS = RHS
