اتحاد مربع کامل:
\[\begin{aligned} (a+b)^2 = a^2 + 2ab + b^2 \end{aligned} \]
طرف چپ
\[\begin{aligned} = (a+b)^2 \end{aligned} \]
\[\begin{aligned} = (a+b) \times (a+b) \end{aligned} \]
\[\begin{aligned} = a^2 + ab + ba + b^2 \end{aligned} \]
اتحاد مربع کامل:
\[\begin{aligned} (a+b)^2 = a^2 + 2ab + b^2 \end{aligned} \]
طرف چپ
\[\begin{aligned} = (a+b)^2 \end{aligned} \]
\[\begin{aligned} = (a+b) \times (a+b) \end{aligned} \]
\[\begin{aligned} = a^2 + ab + ab + b^2 \end{aligned} \]
\[\begin{aligned} = a^2 + 2ab + b^2 \end{aligned} \]
طرف راست
\[\begin{aligned} \sin^2{\theta} + \cos^2{\theta} = 1 \end{aligned} \]
\[\begin{aligned} \sin^2{\theta} = 1 - \cos^2{\theta} \end{aligned} \]
\[\begin{aligned} \cos^2{\theta} = 1 - \sin^2{\theta} \end{aligned} \]
\[\begin{aligned} \sin^2{\theta} + \cos^2{\theta} = 1 \end{aligned} \]
\[\begin{aligned} \sin{\theta} = \pm \sqrt{ 1 - \cos^2{\theta}} \end{aligned} \]
\[\begin{aligned} \cos^2{\theta} = 1 - \sin^2{\theta} \end{aligned} \]
\[\begin{aligned} \sin^2{\theta} + \cos^2{\theta} = 1 \end{aligned} \]
\[\begin{aligned} \sin{\theta} = \pm \sqrt{ 1 - \cos^2{\theta}} \end{aligned} \]
\[\begin{aligned} \cos{\theta} = \pm \sqrt{ 1 - \sin^2{\theta}} \end{aligned} \]
\[\begin{aligned} \tan{\theta} = \dfrac{\sin{\theta}}{\cos{\theta}} \end{aligned} \]
\[\begin{aligned} \cot{\theta} = \dfrac{\cos{\theta}}{\sin{\theta}} \end{aligned} \]
\[\begin{aligned} \tan^2{\theta} + 1 = \dfrac{1}{\cos^2{\theta}} \end{aligned} \]
\[\begin{aligned} \tan{\theta} = \pm \sqrt{\dfrac{1}{\cos^2{\theta}} - 1} \end{aligned} \]
\[\begin{aligned} \cot^2{\theta} + 1 = \dfrac{1}{\sin^2{\theta}} \end{aligned} \]
\[\begin{aligned} \cot{\theta} = \pm \sqrt{\dfrac{1}{\sin^2{\theta}} - 1} \end{aligned} \]