Question

the period of sin3x+cos3x is​

Answer 1

Answer:

By property of periodic function,

f(x+T)=f(x)

∴ assume least possible period i.e.,

2

π

∴f(x+

2

π

)=f(x)

sin

3

x−cos

3

x



=sin

3

x+cos

3

x⇒ wrong assumption

assume → period =π

f(x+π)=f(x)

−sin

3

x−cos

3

x



=sin

3

x+cos

3

x⇒ wrong assumption

assume → period =

2

3π

∴−sin

3

x+cos

3

x



=sin

3

x+cos

3

x⇒ wrong assumption

assume → period =2π

∴sin

3

x+cos

3

x=sin

3

x+cos

3

x correct assumption

This implies, 2π is a period of sin

3

x+cos

3

x.