What is the general solution for cot(x)-2tan(x)=-0.25 ?

The general solution for cot(x)-2tan(x)=-0.25 is x=0.65766…+pin,x=2.56707…+pin

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cot(x)-2tan(x)=-0.25

cot (x) - 2 tan (x) = - 0.25

x = 0.65766 \dots + πn, x = 2.56707 \dots + πn

Solution steps

cot (x) - 2 tan (x) = - 0.25

Subtract

- 0.25

from both sides

cot (x) - 2 tan (x) + 0.25 = 0

Rewrite using trig identities

0.25 + cot (x) - \frac{2}{cot ( x )} = 0

Solve by substitution

cot (x) = \frac{- 1 + 129}{8}, cot (x) = - \frac{1 + 129}{8}

cot (x) = \frac{- 1 + 129}{8} : x = arccot (\frac{- 1 + 129}{8}) + πn

cot (x) = - \frac{1 + 129}{8} : x = arccot (- \frac{1 + 129}{8}) + πn

Combine all the solutions

x = arccot (\frac{- 1 + 129}{8}) + πn, x = arccot (- \frac{1 + 129}{8}) + πn

Show solutions in decimal form

x = 0.65766 \dots + πn, x = 2.56707 \dots + πn

cos (\frac{x}{2}) = \frac{1}{4}

x, y = 2 arcsin (x - 1)

x, - 2 sin (x) - 1 = 0

sin (t) = \frac{1}{8}

sin (θ) - 0.2 \cdot cos (θ) = 0.48979

What is the general solution for cot(x)-2tan(x)=-0.25 ?
The general solution for cot(x)-2tan(x)=-0.25 is x=0.65766…+pin,x=2.56707…+pin