What is the general solution for cot(x)-tan(x)=2sqrt(3) ?

The general solution for cot(x)-tan(x)=2sqrt(3) is x=0.26179…+pin,x=1.83259…+pin

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cot(x)-tan(x)=2sqrt(3)

cot (x) - tan (x) = 23

x = 0.26179 \dots + πn, x = 1.83259 \dots + πn

Solution steps

cot (x) - tan (x) = 23

Subtract

23

from both sides

cot (x) - tan (x) - 23 = 0

Rewrite using trig identities

cot (x) - \frac{1}{cot ( x )} - 23 = 0

Solve by substitution

cot (x) = 3 + 2, cot (x) = 3 - 2

cot (x) = 3 + 2 : x = arccot (3 + 2) + πn

cot (x) = 3 - 2 : x = arccot (3 - 2) + πn

Combine all the solutions

x = arccot (3 + 2) + πn, x = arccot (3 - 2) + πn

Show solutions in decimal form

x = 0.26179 \dots + πn, x = 1.83259 \dots + πn

cos (5 t) cos (3 t) = \frac{1}{2} + sin (- 5 t) sin (3 t)

sin (3 θ + 7 2^{\circ}) = cos (4 8^{\circ}), 0^{\circ} \leq θ \leq 36 0^{\circ}

cot^{2} (y) + csc (y) - 5 = 0

2 cos (θ) = 1, 0 \leq θ < 2 π

cos^{2} (x) - tan (x) cos^{2} (x) = 0

What is the general solution for cot(x)-tan(x)=2sqrt(3) ?
The general solution for cot(x)-tan(x)=2sqrt(3) is x=0.26179…+pin,x=1.83259…+pin