What is the general solution for 2cot(x)-tan(x)+6=8-tan(x) ?

The general solution for 2cot(x)-tan(x)+6=8-tan(x) is x= pi/4+pin

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2cot(x)-tan(x)+6=8-tan(x)

2 cot (x) - tan (x) + 6 = 8 - tan (x)

x = \frac{π}{4} + πn

Degrees

x = 4 5^{\circ} + 18 0^{\circ} n

Solution steps

2 cot (x) - tan (x) + 6 = 8 - tan (x)

Subtract

8 - tan (x)

from both sides

2 cot (x) - 2 = 0

Move

2

to the right side

2 cot (x) - 2 = 0

Add

2

to both sides

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

Simplify

2 cot (x) = 2

2 cot (x) = 2

Divide both sides by

2

2 cot (x) = 2

Divide both sides by

2

\frac{2 cot ( x )}{2} = \frac{2}{2}

Simplify

cot (x) = 1

cot (x) = 1

General solutions for

cot (x) = 1

cot (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

x, 2 sin (x) + 1 = 0

8 tan (3 x) = 8

1 = sin (θ) - cos (θ)

2 - cos (θ) = 2 sin^{2} (θ)

tan (2 x - \frac{π}{6}) = 1, 0 \leq x \leq 2 π

What is the general solution for 2cot(x)-tan(x)+6=8-tan(x) ?
The general solution for 2cot(x)-tan(x)+6=8-tan(x) is x= pi/4+pin