[tex]\bf \textit{Pythagorean Identities}
\\ \quad \\
\boxed{sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta)}
\\ \quad \\
1+cot^2(\theta)=csc^2(\theta)
\\ \quad \\
1+tan^2(\theta)=sec^2(\theta)
\\\\\\
and\qquad \qquad tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\\\\
-----------------------------\\\\[/tex]
[tex]\bf tan(\theta)[1-sin^2(\theta)]=sin(\theta)cos(\theta)\\\\
-----------------------------\\\\
tan(\theta)\boxed{cos^2(\theta)}\implies \cfrac{sin(\theta)}{cos(\theta)}\cdot cos^2(\theta)
\implies sin(\theta)cos(\theta)[/tex]
