Differential Calculus | Engineering Mathematics

Solution

\(\tan \theta = \dfrac{\sin \theta}{\cos \theta}\)

\(\dfrac{d(\tan \theta)}{d\theta} = \dfrac{d(\dfrac{\sin \theta}{\cos \theta})}{d\theta}\)

\(\dfrac{d(\tan \theta)}{d\theta} = \frac{\cos \theta (\cos \theta d\theta) - \sin \theta (-\sin \theta d\theta)}{\cos^2 \theta}\)

\(\dfrac{d(\tan \theta)}{d\theta} =\dfrac{\cos^2 \theta + \sin^2 \theta}{\cos^2 \theta} (d\theta)\)

\(\dfrac{d(\tan \theta)}{d\theta} = \dfrac{1}{\cos^2 \theta} (d\theta)\)

\(\dfrac{d(\tan \theta)}{d\theta} = \sec \theta \; d\theta \)