Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)
A
sec2 \(\theta\)
B
tan \(\theta\) cosec \(\theta\)
C
cosec \(\theta\)sec \(\theta\)
D
cosec2\(\theta\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
\(\frac {\sin\theta}{\cos\theta}\)
\(\frac{\cos \theta {\frac{d(\sin \theta)}{d \theta}} - \sin \theta {\frac{d(\cos \theta)}{d \theta}}}{\cos^2 \theta}\)
\(\frac{\cos \theta. \cos \theta - \sin \theta (-\sin \theta)}{cos^2\theta}\)
\(\frac{cos^2\theta + \sin^2 \theta}{cos^2\theta}\)
Recall that sin2 \(\theta\) + cos2 \(\theta\) = 1
\(\frac{1}{\cos^2\theta}\) = sec2 \(\theta\)
Source: Myschool Past Questions Archive (Record #29536)