Functions Question 719
Question: The graph of the function $ \cos x,\cos ,(x+2)-cos^{2}(x+1) $ is
Options:
A) A straight line passing through $ (0,-sin^{2}1) $ with slope 2
B) A straight line passing through (0, 0)
C) A parabola with vertex $ (1,-sin^{2}1) $
D) A straight line passing through the point $ ( \frac{\pi }{2},-{{\sin }^{2}}1 ) $ and parallel to the x-axis.
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Answer:
Correct Answer: D
Solution:
[d] $ y=\frac{1}{2}[cos(2x+2)+cos2-{1+cos(2x+2)}] $ Or $ y=-\frac{1}{2},(1-cos2)=-sin^{2}1 $ i.e. constant
$ \therefore $ Graph is a line parallel to x-axis. Also when $ x=\frac{\pi }{2},y=-{{\cos }^{2}}( \frac{\pi }{2}+1 )=-{{\sin }^{2}}1 $ and hence it passes through the point $ ( \frac{\pi }{2},-{{\sin }^{2}}1 ) $
BETA
