What is the general solution for 1/(tan(x))-2tan(x)=-1/4 ?

The general solution for 1/(tan(x))-2tan(x)=-1/4 is x=-0.57451…+pin,x=0.65766…+pin

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1/(tan(x))-2tan(x)=-1/4

\frac{1}{tan ( x )} - 2 tan (x) = - \frac{1}{4}

x = - 0.57451 \dots + πn, x = 0.65766 \dots + πn

Solution steps

\frac{1}{tan ( x )} - 2 tan (x) = - \frac{1}{4}

Solve by substitution

tan (x) = - \frac{- 1 + 129}{16}, tan (x) = \frac{1 + 129}{16}

tan (x) = - \frac{- 1 + 129}{16} : x = arctan (- \frac{- 1 + 129}{16}) + πn

tan (x) = \frac{1 + 129}{16} : x = arctan (\frac{1 + 129}{16}) + πn

Combine all the solutions

x = arctan (- \frac{- 1 + 129}{16}) + πn, x = arctan (\frac{1 + 129}{16}) + πn

Show solutions in decimal form

x = - 0.57451 \dots + πn, x = 0.65766 \dots + πn

tan (a) = \frac{3}{2}

cos (x + \frac{π}{6}) = - 1

tan (4 x + 20) \cdot cot (x + 5 0^{\circ}) = 1

csc (x) = - 0.5

cos (θ) - 4 = - 3

What is the general solution for 1/(tan(x))-2tan(x)=-1/4 ?
The general solution for 1/(tan(x))-2tan(x)=-1/4 is x=-0.57451…+pin,x=0.65766…+pin