Question

the Damian of function f (×)
sin 3× + cos 3× is​

Answer 1

Answer:

Step-by-step explanation:

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.