Find the derivative of frac sin theta cos theta - JAMB Mathematics 2011 Question

(\frac {\sin\theta}{\cos\theta})

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

(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta})

(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta})

Recall that sin² (\theta) + cos² (\theta) = 1

(\frac{1}{\cos^2\theta}) = sec² (\theta)