What is the general solution for solvefor x,arctan(1/x)=80 ?

The general solution for solvefor x,arctan(1/x)=80 is x= 1/(tan(80))

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solvefor x,arctan(1/x)=80

solve for

x, arctan (\frac{1}{x}) = 8 0^{\circ}

x = \frac{1}{tan ( 8 0 ^{\circ} )}

Solution steps

arctan (\frac{1}{x}) = 8 0^{\circ}

Apply trig inverse properties

arctan (\frac{1}{x}) = 8 0^{\circ}

arctan (x) = a \Rightarrow x = tan (a)

\frac{1}{x} = tan (8 0^{\circ})

\frac{1}{x} = tan (8 0^{\circ})

Solve

\frac{1}{x} = tan (8 0^{\circ}) : x = \frac{1}{tan ( 8 0 ^{\circ} )}

\frac{1}{x} = tan (8 0^{\circ})

Multiply both sides by

x

\frac{1}{x} = tan (8 0^{\circ})

Multiply both sides by

x

\frac{1}{x} x = tan (8 0^{\circ}) x

Simplify

1 = tan (8 0^{\circ}) x

1 = tan (8 0^{\circ}) x

Switch sides

tan (8 0^{\circ}) x = 1

Divide both sides by

tan (8 0^{\circ})

tan (8 0^{\circ}) x = 1

Divide both sides by

tan (8 0^{\circ})

\frac{tan ( 8 0 ^{\circ} ) x}{tan ( 8 0 ^{\circ} )} = \frac{1}{tan ( 8 0 ^{\circ} )}

Simplify

x = \frac{1}{tan ( 8 0 ^{\circ} )}

x = \frac{1}{tan ( 8 0 ^{\circ} )}

Verify Solutions

Find undefined (singularity) points:

x = 0

Take the denominator(s) of

\frac{1}{x}

and compare to zero

x = 0

The following points are undefined

x = 0

Combine undefined points with solutions:

x = \frac{1}{tan ( 8 0 ^{\circ} )}

x = \frac{1}{tan ( 8 0 ^{\circ} )}

2 sin (θ) cos (θ) + 2 sin (θ) + cos (θ) + 1 = 0

cos (x) - cos (2 x) = 0, 0 \leq x \leq 2 π

sin (t) + 2 sin (2 t) = 0

1 + cos (θ) = 0

x, (D^{2} - 3 D + 2) y = cos (e^{- x})

What is the general solution for solvefor x,arctan(1/x)=80 ?
The general solution for solvefor x,arctan(1/x)=80 is x= 1/(tan(80))