What is the domain of (sin(4t)-sin(2t))/(cos(4t)-cos(2t)) ?

The domain of (sin(4t)-sin(2t))/(cos(4t)-cos(2t)) is pi/3 n<t< pi/3+pi/3 n

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domain of (sin(4t)-sin(2t))/(cos(4t)-cos(2t))

domain

\frac{sin ( 4 t ) - sin ( 2 t )}{cos ( 4 t ) - cos ( 2 t )}

\frac{π}{3} n < t < \frac{π}{3} + \frac{π}{3} n

Interval Notation

(\frac{π}{3} n, \frac{π}{3} + \frac{π}{3} n)

Solution steps

Take the denominator(s) of

\frac{sin ( 4 t ) - sin ( 2 t )}{cos ( 4 t ) - cos ( 2 t )}

and compare to zero:

t = \frac{π}{3} n

Periodicity of

\frac{sin ( 4 t ) - sin ( 2 t )}{cos ( 4 t ) - cos ( 2 t )} : \frac{π}{3}

Combine period:

\frac{π}{3} n \leq t < \frac{π}{3} + \frac{π}{3} n

and undefined points.

The domain is

\frac{π}{3} n < t < \frac{π}{3} + \frac{π}{3} n

f (x) = \frac{x}{x ^{2} - 225}

k (x) = \frac{x + 3}{x - 1}

f (x) = x^{3} - 12 x^{2} + 45 x - 54

\frac{∣ x ∣}{∣ x ∣ - 5}

f (x) = 3^{x - 3}

What is the domain of (sin(4t)-sin(2t))/(cos(4t)-cos(2t)) ?
The domain of (sin(4t)-sin(2t))/(cos(4t)-cos(2t)) is pi/3 n<t< pi/3+pi/3 n