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Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)...

Find the derivative of \(\frac {\sin\theta}{\cos\theta}\)

A.

sec2 \(\theta\)

B.

tan \(\theta\) cosec \(\theta\)

C.

cosec \(\theta\)sec \(\theta\)

D.

cosec2\(\theta\)

Correct answer is A

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

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

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

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

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

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