Question

# The period of f(x) = [sin 5x] + |cos 6x| is -

- 2

Hint:

### In this question we have to find the period of f(x) = [sin 5x] + |cos 6x|. Here [.] is greatest integer function and | is modulus function. Find the each individual function’s period and then take LCM of both function .

## The correct answer is: 2

### Here we have to find the solution of period of f(x) = [sin5x] + |cos 6x|.

Firstly, we are given two function, first is greater integer function and second is modulus function.

We have, f(x) = [sin 5x] + |cos 6x|

f(x) = f1(x) + f2(x)

For greater integer function,

f1(x) = [sin 5x]

period of f1(x) = [sin 5x]

we know that the period of sinx → 2π

period of [sin 5x] = [sin ( 5x + 2π) ]

period of f1(x) = [sin 5 ( x + 2π/5)]

therefore the period of f1(x) = 2 π/5 =

For modulus function,

f2(x) = | cos 6x |

we know that period of cosx → π

period of f2(x) = |cos 6x| = |cos 6x + π|

= |cos 6( x + π/6)|

Therefore, Period of f2(x) = π/6

Now, LCM of 2 π/5 and π/6 = 2π

Therefore, the correct answer is 2π.

In this question , we have to find the period of f(x) = [sin 5x] + |cos 6x|. We know that sinx period is 2 π and cosx is π. we know that if sin(x + a) then a is period so find the a both in sin and cos and then take both LCM.

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