Question

how do you simplify (2cos(t))^2+(3sin(t))^2

Answer 1

Cos sqaured t is 1 minus sin squared t. So sub that in and simplify i suppose?

Answer 2

\[\begin{align*}(2\cos t)^2+(3\sin t)^2&=4\cos^2t+9\sin^2t\\
&=(4\cos^2t+4\sin^2t)+5\sin^2t\\
&=4(\cos^2t+\sin^2t)+5\sin^2t
\end{align*}\]