Simplify: (frac{cos 2theta – 1}{sin 2theta})
-
A.
(-tan theta) -
B.
(-cos theta) -
C.
(tan theta) -
D.
(cos theta)
Correct Answer: Option A
Explanation
(frac{cos 2theta – 1}{sin 2theta})
(cos (x + y) = cos x cos y – sin x sin y implies cos 2theta = cos^{2} theta – sin^{2} theta)
(cos^{2} theta = 1 – sin^{2} theta implies cos 2theta = 1 – 2sin^{2} theta)
(sin 2theta = 2sin theta cos theta)
(therefore frac{cos 2theta – 1}{sin 2theta} = frac{1 – 2sin^{2}theta – 1}{2sin theta cos theta})
= (frac{-2 sin^{2} theta}{2sin theta cos theta} = frac{- sin theta}{cos theta})
= (-tan theta)