If (2sin^{2}theta = 1 + cos theta, 0° leq theta leq 90°), find (theta).
-
A.
30° -
B.
45° -
C.
60° -
D.
90°
Correct Answer: Option C
Explanation
(2sin^{2}theta = 1 + cos theta implies 2(1 – cos^{2}theta) = 1 + cos theta)
(2 – 2cos^{2}theta = 1 + cos theta)
(2 – 2cos^{2}theta – 1 – cos theta = 0)
(2cos^{2}theta + cos theta – 1 = 0)
(2cos^{2}theta + 2costheta – cos theta – 1 = 0 implies 2cos theta(cos theta + 1) – 1(cos theta + 1) = 0)
((2cos theta – 1)(cos theta + 1) = 0 implies cos theta = frac{1}{2} )
(theta = cos^{-1} frac{1}{2} = 60°)