# Derivatives of Secant and Cosecant $\frac d {d\theta} \bigg [ \sec \theta \bigg] = \sec \theta \tan \theta$ $\frac d {d\theta} \bigg [ \csc \theta \bigg] = -\csc \theta \cot \theta$ ^fc25n3 $\frac d {d\theta} \bigg [ \sec \theta \bigg] = \frac d {d\theta} \bigg [ \frac 1 {\cos \theta} \bigg] = -\cos^{-2} \theta \cdot (- \sin \theta)=\frac {\sin\theta} {\cos^2\theta}=\sec \theta\tan \theta$ $\frac d {d\theta} \bigg [ \csc \theta \bigg] = \frac d {d\theta} \bigg [ \frac 1 {\sin \theta} \bigg] = -\sin^{-2} \theta \cdot \cos \theta=-\frac {\cos\theta} {\sin^2\theta}=-\csc \theta\cot \theta$