\[sin^2θ\ +\ cos^2θ\ =\ 1\ \hspace{10cm}\]
\[1\ +\ tan^2θ\ =\ sec^2θ\ \hspace{10cm}\]
\[1\ +\ cot^2θ\ =\ cosec^2θ\ \hspace{10cm}\]
\[Sin ( A + B )\ =\ Sin A\ Cos B\ +\ Cos A\ Sin B\]
\[Sin ( A – B )\ =\ Sin A\ Cos B\ -\ Cos A\ Sin B\]
\[Cos( A + B )\ =\ Cos A\ Cos B\ -\ Sin A Sin B\]
\[Cos( A – B )\ =\ Cos A\ Cos B\ +\ Sin A Sin B\]
\[Tan(A + B)\ =\ \frac{Tan A\ +\ Tan B}{1\ -\ Tan A\ Tan B}\]
\[Tan(A – B)\ =\ \frac{Tan A\ -\ Tan B}{1\ +\ Tan A\ Tan B}\]
\[\color {brown} {Note}:\ Sin\ ( – θ )\ =\ -\ sin\ θ\ \hspace{2cm}\ cos\ ( – θ )\ =\ cos\ θ\]
\[\color {royalblue} {Multiple\ Angles\ of\ 2A}:\ \hspace{20cm}\]
\[1\ (i)\ Sin\ 2A\ =\ 2\ Sin\ A\ Cos\ A\ \hspace{5cm}\ (ii)\ Sin\ 2A\ =\ \frac{2\ Tan\ A}{1\ +\ Tan^2\ A}\]
\[2\ (i)\ Cos\ 2A\ =\ Cos^2A\ -\ Sin^2A\ \hspace{5cm}\ (ii)\ Cos\ 2A\ =\ \frac{1\ -\ Tan^2A}{1\ +\ Tan^2\ A}\]
\[3.\ Tan\ 2A\ =\ \frac{2\ Tan\ A}{1\ -\ Tan^2\ A}\ \hspace{10cm}\]
\[4.\ Sin^2A\ =\ \frac{1\ -\ Cos\ 2A}{2}\ \hspace{5cm}\ Note:\ 1\ -\ 2\ Sin^2A\ =\ Cos\ 2A\]
\[5.\ Cos^2A\ =\ \frac{1\ +\ Cos\ 2A}{2}\ \hspace{10cm}\]
\[6.\ Tan^2A\ =\ \frac{1\ -\ Cos\ 2A}{1\ +\ Cos\ 2A}\ \hspace{10cm}\]