Question

THE PERIOD OF sin^3x+cos^3x is

Answer 1

By property of periodic function,

f(x+T)=f(x)

∴ assume least possible period i.e., 2π​

∴f(x+2π​)=f(x)

sin^3x−cos^3x ≠ sin^3x+cos^3x⇒ wrong assumption

assume → period =π

f(x+π)=f(x)

−sin^3x−cos^3x ≠ sin^3x+cos^3x⇒ wrong assumption

assume → period =3π/2​

∴−sin^3x+cos^3x ≠ sin^3x+cos^3x⇒ wrong assumption

assume → period =2π

∴sin^3x+cos^3x=sin^3x+cos^3x correct assumption

This implies, 2π is a period of sin3x+cos3x.

TAKE CARE.

HOPE THIS WILL HELP YOU.