What is the general solution for solvefor x,tan(x*y!)=1 ?

The general solution for solvefor x,tan(x*y!)=1 is x= pi/(4y!)+(pin)/(y!);\quad x!\ne 0

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solvefor x,tan(x*y!)=1

solve for

x, tan (x \cdot y!) = 1

x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

Solution steps

tan (x y!) = 1

General solutions for

tan (x y!) = 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x y! = \frac{π}{4} + πn

x y! = \frac{π}{4} + πn

Solve

x y! = \frac{π}{4} + πn : x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

x y! = \frac{π}{4} + πn

Divide both sides by

y!; x! \neq = 0

x y! = \frac{π}{4} + πn

Divide both sides by

y!; x! \neq = 0

\frac{x y !}{y !} = \frac{\frac{π}{4}}{y !} + \frac{πn}{y !}; x! \neq = 0

Simplify

\frac{x y !}{y !} = \frac{\frac{π}{4}}{y !} + \frac{πn}{y !}

Simplify

\frac{x y !}{y !} : x

\frac{x y !}{y !}

Cancel the common factor:

y!

= x

Simplify

\frac{\frac{π}{4}}{y !} + \frac{πn}{y !} : \frac{π}{4 y !} + \frac{πn}{y !}

\frac{\frac{π}{4}}{y !} + \frac{πn}{y !}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

= \frac{π}{4 y !} + \frac{πn}{y !}

x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

x = \frac{π}{4 y !} + \frac{πn}{y !}; x! \neq = 0

sec^{2} (x) - 5 sec (x) = 0

8 sin (x) cos (x) = 12

cos (x) = \frac{1}{5}

3 tan (3 x) + 1 = 0

2 tan (θ) - 3 = 0

What is the general solution for solvefor x,tan(x*y!)=1 ?
The general solution for solvefor x,tan(x*y!)=1 is x= pi/(4y!)+(pin)/(y!);\quad x!\ne 0