Find the derivative of (frac {sintheta}{costheta})

A.
sec^{2} (theta) 
B.
tan (theta) cosec (theta) 
C.
cosec (theta)sec (theta) 
D.
cosec^{2}(theta)
Correct Answer: Option A
Explanation
(frac {sintheta}{costheta})
(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^2theta})
(frac{cos^2theta + sin^2 theta}{cos^2theta})
Recall that sin^{2} (theta) + cos^{2} (theta) = 1
(frac{1}{cos^2theta}) = sec^{2} (theta)