Question

Find the integral of (tan(theta)-1)^2 d*theta.

Answer 1

first expand the bracket:
\[\int\limits_{}^{}(\tan(\theta) - 1)^2 d\theta = \int\limits_{}^{}[ \tan^2(\theta) - 2\tan(\theta) + 1] d\theta\]use the trig id: sec^2(x) = tan^2(x) + 1
\[\int\limits_{}^{}[\sec^2(\theta) + 2\tan(\theta)]d\theta\]
lmk if i need to keep going ^_^