The function f x = sin 4 x + cos 2 x , is a periodic function with a fundamental period

Step-by-step solution

Given f x = sin 4 x + cos 2 x We know that the period of sin x is π and also if f x is a periodic function with fundamental period T , then the fundamental period of f k x is T k . ⇒ T 1 = period of sin4 x = π 4 Also, we know that the period of cos x is π ⇒ T 2 = Period of cos 2 x = π 2 Again, we know that the period of the sum or difference of two periodic functions is the L . C . M . of their periods. So, the period of f ( x ) is L . C . M . of the periods of sin 4 x and cos 2 x i.