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Joint Entrance Examination
Mathematics
Trigonometric Ratios and Identities
Question 276
Question 276 of 298
Medium
MCQ
Which one is not periodic?
A
∣
sin
3
x
∣
+
sin
2
x
|\sin3x|+\sin^2x
∣
sin
3
x
∣
+
sin
2
x
B
cos
x
+
cos
2
x
\cos\sqrt x+\cos^2x
cos
x
+
cos
2
x
C
cos
4
x
+
tan
2
x
\cos4x+\tan^2x
cos
4
x
+
tan
2
x
D
cos
2
x
+
sin
x
\cos2x+\sin x
cos
2
x
+
sin
x
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Solutions · 1
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Official solution
cos
x
\cos\sqrt x
cos
x
is not periodic (since
x
\sqrt x
x
is not a linear/periodic-compatible argument), so the sum
cos
x
+
cos
2
x
\cos\sqrt x+\cos^2x
cos
x
+
cos
2
x
cannot be periodic --- no matter how "nice"
cos
2
x
\cos^2x
cos
2
x
is on its own, the non-periodic term dominates.
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