Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)
A. sec
2 \(\theta\)
B. tan \(\theta\) cosec \(\theta\)
C. cosec \(\theta\)sec \(\theta\)
D. cosec
2\(\theta\)
Correct Answer: A
Explanation
\(\frac {\sin\theta}{\cos\theta}\)
\(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\)
\(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\)
\(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\)
Recall that sin2 \(\theta\) + cos2 \(\theta\) = 1
\(\frac{1}{\cos^2\theta}\) = sec2 \(\theta\)
