What is the periodicity of f(x)=csc(4x)-csc(8x)-cot(8x) ?

The periodicity of f(x)=csc(4x)-csc(8x)-cot(8x) is pi

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periodicity of f(x)=csc(4x)-csc(8x)-cot(8x)

periodicity

f (x) = csc (4 x) - csc (8 x) - cot (8 x)

π

Solution steps

The compound periodicity of the sum of periodic functions is the least common multiplier of the periods

csc (4 x), csc (8 x), cot (8 x)

Periodicity of

csc (4 x) : \frac{π}{2}

Periodicity of

csc (8 x) : \frac{π}{4}

Periodicity of

cot (8 x) : \frac{π}{8}

Combine periods:

\frac{π}{2}, \frac{π}{4}, \frac{π}{8}

= π

f (x) = 7 x - 40

f (t) = \frac{6 t - 3}{5 t + 8}

f (x) = - 4 x^{\frac{1}{2}}

f (A) = tan^{2} (A)

y = 3 - \frac{1}{3} x^{2}

What is the periodicity of f(x)=csc(4x)-csc(8x)-cot(8x) ?
The periodicity of f(x)=csc(4x)-csc(8x)-cot(8x) is pi