Class 12
\[\begin{align*} 1 - \cos^2 t &= \sin^2 t\\ 1 - \sin^2 t &= \cos^2 t\\ 1 + \tan^2 t &= \sec^2 t\\ \sec^2 t - 1 &= \tan^2 t \end{align*}\]
\(\displaystyle \int x^2\sqrt{x^2 + 9}\;dx\)
\(\displaystyle \int \frac{1}{\sqrt{x^2 - 9}}\;dx\)
\(\displaystyle \int \frac{1}{x^2}\sqrt{7 - x^2}\;dx\)
If \(x = \sqrt{3}\cos t\), express each of the following in terms of \(x\):
\(\sin t\)
\(\sin 2t\)
\(\tan t\)
If \(x = 5\tan t\), express each of the following in terms of \(x\):
\(\sin t\)
\(\sec t\)
\(\displaystyle \int \frac{1}{\sqrt{x^2 - 9}}\;dx\)
\(\displaystyle \int x^2\sqrt{x^2 + 9}\;dx\)