What is the general solution for -1=(tan(x)-(3/4))/(1+tan(x)(3/4)) ?

The general solution for -1=(tan(x)-(3/4))/(1+tan(x)(3/4)) is x=-0.14189…+pin

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-1=(tan(x)-(3/4))/(1+tan(x)(3/4))

- 1 = \frac{tan ( x ) - ( \frac{3}{4} )}{1 + tan ( x ) ( \frac{3}{4} )}

x = - 0.14189 \dots + πn

Solution steps

- 1 = \frac{tan ( x ) - ( \frac{3}{4} )}{1 + tan ( x ) ( \frac{3}{4} )}

Switch sides

\frac{tan ( x ) - \frac{3}{4}}{1 + tan ( x ) \frac{3}{4}} = - 1

Solve by substitution

tan (x) = - \frac{1}{7}

tan (x) = - \frac{1}{7} : x = arctan (- \frac{1}{7}) + πn

Combine all the solutions

x = arctan (- \frac{1}{7}) + πn

Show solutions in decimal form

x = - 0.14189 \dots + πn

cos (x) = - \frac{15}{13}

arctan (\frac{20}{x}) - arctan (\frac{400}{x}) = - 9.72

cos (θ) = \frac{9}{15}

tan (t) = - \frac{5}{12}

1 - 3 cos (x) - cos (2 x) = 0

What is the general solution for -1=(tan(x)-(3/4))/(1+tan(x)(3/4)) ?
The general solution for -1=(tan(x)-(3/4))/(1+tan(x)(3/4)) is x=-0.14189…+pin