# Derivatives of Tangent and Cotangent $\frac d {d\theta} \bigg [ \tan \theta \bigg] = \sec^2 \theta$ $\frac d {d\theta} \bigg [ \cot \theta \bigg] = -\csc^2 \theta$^0ytid3 $\frac d {d\theta} \bigg [ \tan \theta \bigg] = \frac d {d\theta} \bigg [ \frac {\sin \theta} {\cos \theta} \bigg] = \frac {\cos^2 \theta + \sin^2 \theta} {\cos ^2 \theta} = \frac 1 {\cos^2 \theta}$ $\frac d {d\theta} \bigg [ \cot \theta \bigg] = \frac d {d\theta} \bigg [ \frac {\cos \theta} {\sin \theta} \bigg] = -\frac {\sin^2 \theta + \cos^2 \theta} {\sin ^2 \theta} = -\frac 1 {\sin^2 \theta}$