What is the general solution for -11tan(x)+1=-2(4+tan(x)) ?

The general solution for -11tan(x)+1=-2(4+tan(x)) is x= pi/4+pin

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-11tan(x)+1=-2(4+tan(x))

Solution

- 11 tan (x) + 1 = - 2 (4 + tan (x))

Solution

x = \frac{π}{4} + πn

Degrees

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

Solution steps

- 11 tan (x) + 1 = - 2 (4 + tan (x))

Solve by substitution

- 11 tan (x) + 1 = - 2 (4 + tan (x))

Let:

tan (x) = u

- 11 u + 1 = - 2 (4 + u)

- 11 u + 1 = - 2 (4 + u) : u = 1

- 11 u + 1 = - 2 (4 + u)

Expand

- 2 (4 + u) : - 8 - 2 u

- 2 (4 + u)

Apply the distributive law:

a (b + c) = ab + a c

a = - 2, b = 4, c = u

= - 2 \cdot 4 + (- 2) u

Apply minus-plus rules

+ (- a) = - a

= - 2 \cdot 4 - 2 u

Multiply the numbers:

2 \cdot 4 = 8

= - 8 - 2 u

- 11 u + 1 = - 8 - 2 u

Move

1

to the right side

- 11 u + 1 = - 8 - 2 u

Subtract

1

from both sides

- 11 u + 1 - 1 = - 8 - 2 u - 1

Simplify

- 11 u = - 2 u - 9

- 11 u = - 2 u - 9

Move

2 u

to the left side

- 11 u = - 2 u - 9

Add

2 u

to both sides

- 11 u + 2 u = - 2 u - 9 + 2 u

Simplify

- 9 u = - 9

- 9 u = - 9

Divide both sides by

- 9

- 9 u = - 9

Divide both sides by

- 9

\frac{- 9 u}{- 9} = \frac{- 9}{- 9}

Simplify

u = 1

u = 1

Substitute back

u = tan (x)

tan (x) = 1

tan (x) = 1

tan (x) = 1 : x = \frac{π}{4} + πn

tan (x) = 1

General solutions for

tan (x) = 1

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{π}{4} + πn

x = \frac{π}{4} + πn

Combine all the solutions

x = \frac{π}{4} + πn

Popular Examples

16=-10cos((2pi)/(150)t)+10

16 = - 10 cos (\frac{2 π}{150} t) + 10

2cos(x)-sqrt(3)=0,0<= x<= 2pi

2 cos (x) - 3 = 0, 0 \leq x \leq 2 π

sec^2(x)-1=0,0<= x<= 2pi

sec^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

3cos(x/2)+sqrt(3)=cos(x/2)

3 cos (\frac{x}{2}) + 3 = cos (\frac{x}{2})

(tan(θ)+1)(tan(θ)-sqrt(3))=0

(tan (θ) + 1) (tan (θ) - 3) = 0

Frequently Asked Questions (FAQ)

What is the general solution for -11tan(x)+1=-2(4+tan(x)) ?
The general solution for -11tan(x)+1=-2(4+tan(x)) is x= pi/4+pin