What is the general solution for 4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x) ?

The general solution for 4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x) is x= pi/4+pin

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Popular Trigonometry >

4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x)

Solution

42 tan (x) - 2 = 32 tan (x)

Solution

x = \frac{π}{4} + πn

Degrees

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

Solution steps

42 tan (x) - 2 = 32 tan (x)

Solve by substitution

42 tan (x) - 2 = 32 tan (x)

Let:

tan (x) = u

42 u - 2 = 32 u

42 u - 2 = 32 u : u = 1

42 u - 2 = 32 u

Move

2

to the right side

42 u - 2 = 32 u

Add

2

to both sides

42 u - 2 + 2 = 32 u + 2

Simplify

42 u = 32 u + 2

42 u = 32 u + 2

Move

32 u

to the left side

42 u = 32 u + 2

Subtract

32 u

from both sides

42 u - 32 u = 32 u + 2 - 32 u

Simplify

42 u - 32 u = 32 u + 2 - 32 u

Simplify

42 u - 32 u : 2 u

42 u - 32 u

Add similar elements:

42 u - 32 u = 2 u

= 2 u

Simplify

32 u + 2 - 32 u : 2

32 u + 2 - 32 u

Add similar elements:

32 u - 32 u = 0

= 2

2 u = 2

2 u = 2

2 u = 2

Divide both sides by

2

2 u = 2

Divide both sides by

2

\frac{2 u}{2} = \frac{2}{2}

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

Graph

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Frequently Asked Questions (FAQ)

What is the general solution for 4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x) ?
The general solution for 4sqrt(2)tan(x)-sqrt(2)=3sqrt(2)tan(x) is x= pi/4+pin