Find the derivative of (frac {sintheta}{costheta})
-
A.
sec2 (theta) -
B.
tan (theta) cosec (theta) -
C.
cosec (theta)sec (theta) -
D.
cosec2(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 sin2 (theta) + cos2 (theta) = 1
(frac{1}{cos^2theta}) = sec2 (theta)