If (2sin^{2} theta = 1 + cos theta, 0° leq theta leq 90°), find the value of (theta).
-
A.
90° -
B.
60° -
C.
45° -
D.
30°
Correct Answer: Option B
Explanation
(2sin^{2} theta = 1 + cos theta)
(2 ( 1 – cos^{2} theta) = 1 + cos theta)
(2 – 2cos^{2} theta = 1 + cos theta)
(0 = 1 – 2 + cos theta + 2cos^{2} theta)
(2cos^{2} theta + cos theta – 1 = 0)
Factorizing, we have
((cos theta + 1)(2cos theta – 1) = 0)
Note: In the range, (0° leq theta leq 90°), all trig functions are positive, so we consider
(2cos theta = 1 implies cos theta = frac{1}{2})
(theta = 60°).