What is the f(x)=(sin(x)+cos(x))/(cos(2x)) ?

The f(x)=(sin(x)+cos(x))/(cos(2x)) is

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f(x)=(sin(x)+cos(x))/(cos(2x))

f (x) = \frac{sin ( x ) + cos ( x )}{cos ( 2 x )}

Period : 2 π

Domain : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range : f (x) < - \frac{1}{2} or f (x) > \frac{1}{2}

Y Intercepts : (0, 1)

Asymptotes : Vertical x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points : None

Interval Notation

Domain : [2 πn, \frac{π}{4} + 2 πn) \cup (\frac{π}{4} + 2 πn, \frac{3 π}{4} + 2 πn) \cup (\frac{3 π}{4} + 2 πn, \frac{5 π}{4} + 2 πn) \cup (\frac{5 π}{4} + 2 πn, \frac{7 π}{4} + 2 πn) \cup (\frac{7 π}{4} + 2 πn, 2 π + 2 πn)

Range : (- \infty, - \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Periodicity of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} : 2 π

Domain of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} : 2 πn \leq x < \frac{π}{4} + 2 πn or \frac{π}{4} + 2 πn < x < \frac{3 π}{4} + 2 πn or \frac{3 π}{4} + 2 πn < x < \frac{5 π}{4} + 2 πn or \frac{5 π}{4} + 2 πn < x < \frac{7 π}{4} + 2 πn or \frac{7 π}{4} + 2 πn < x < 2 π + 2 πn

Range of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} : f (x) < - \frac{1}{2} or f (x) > \frac{1}{2}

Axis interception points of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} :

Y Intercepts

: (0, 1)

Asymptotes of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} :

Vertical

: x = \frac{5 π}{4} + 2 πn, x = \frac{π}{4} + 2 πn

Extreme Points of

\frac{sin ( x ) + cos ( x )}{cos ( 2 x )} :

None

What is the f(x)=(sin(x)+cos(x))/(cos(2x)) ?
The f(x)=(sin(x)+cos(x))/(cos(2x)) is