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period of f(x)=sin 4 x+cos 4 x is???????????????????????????

period of f(x)=sin4x+cos4x is???????????????????????????

Grade:12th pass

2 Answers

P srivadhan
26 Points
4 years ago
The period of  sin4x  is 2π
The period of cos4x is 2π
The period of sinnx is 2π
The period of cosnx is 2π
If f(x) = g(x) +h(x) then the period of f(x) is the LCM of periods of g(x) and h(x)
So , The period of  f(x)=sin4x+cos4x is LCM of 2π and 2π i.e…. 2π.
Answer : 2π.
                                                                                Thank you.
Gopal Gopakumar
27 Points
4 years ago
This equation can be written as (sin2x + cos2x )2 – 2sin2xcos2x
which is 1 – 2sin2xcos2x..... multiplying and dividing with 4 gives,
(4 – 8sin2xcos2x)/4 which using sin2@ identity can be written as
(4 – 2sin22x)/4 = (3 + 1 – 2sin22x)/4
which by cos2@ identity gives,
(3 + cos4x)/4 and hence is the simplified equation.
period od cos(n)x = 2pi/n
so period of cos4x = pi/2

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