Period of sin4(x) + cos4(x): Find the Answer Here

[phymatter]

i have to find the period of sin⁴(x) + cos⁴(x)

i know that the period of both the functions individually is pi , but i am unable to find the period of sum of these two functions..

pl. help!

 

[losiu99]

sin⁴(x) + cos⁴(x)=(sin²x+cos²x)²-2sin²x cos²x=2-1\2 sin²(2x).

 

[phymatter]

sin⁴(x) + cos⁴(x)=(sin²x+cos²x)²-2sin²x cos²x=2-1\2 sin²(2x).

by this we get the period as pi/2 , and that's correct ,
but why can't we get this answer by finding the lcm of the period of two functions?
by that we get ans as pi!

 

[HallsofIvy]

Why should that give the period?

 

[CRGreathouse]

finding the lcm of the period of two functions

This gives a multiple of the period.

 

[RobertT]

One way to find the period is by re-expressing the function with Euler's formula and then simplify and re-express it back into a trigonometric function.

Period of the function is pi/2