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Question:

The function f(x) = |sin4x| + |cos2x| is a periodic function with period

π

π4

2π

π2

Solution:

Given f(x) = |sin4x| + |cos2x| = √sin²4x + √cos²2x = √(1 - cos8x)/2 + √(1 + cos4x)/2
Now, period of = √(1 - cos8x)/2 is π/4
Period of = √(1 + cos4x)/2 is π/2.
LCM of π/4 and π/2 is π/2.
Hence, period of f(x) is π/2.