What is the general solution for 4tan(x)-7=3tan(x)-6 ?

The general solution for 4tan(x)-7=3tan(x)-6 is x= pi/4+pin

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4tan(x)-7=3tan(x)-6

4 tan (x) - 7 = 3 tan (x) - 6

x = \frac{π}{4} + πn

Degrees

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

Solution steps

4 tan (x) - 7 = 3 tan (x) - 6

Solve by substitution

4 tan (x) - 7 = 3 tan (x) - 6

Let:

tan (x) = u

4 u - 7 = 3 u - 6

4 u - 7 = 3 u - 6 : u = 1

4 u - 7 = 3 u - 6

Move

7

to the right side

4 u - 7 = 3 u - 6

Add

7

to both sides

4 u - 7 + 7 = 3 u - 6 + 7

Simplify

4 u = 3 u + 1

4 u = 3 u + 1

Move

3 u

to the left side

4 u = 3 u + 1

Subtract

3 u

from both sides

4 u - 3 u = 3 u + 1 - 3 u

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

2 sin^{2} (x) + 1 = 0

sin (x + \frac{π}{4}) - sin (x - \frac{π}{4}) = 0

so l v e f or x, arcsin (y) = arcsin (x) + \frac{( π )}{4}

18 sin^{2} (x) - 9 sin (x) = 0

cos (\frac{π x}{2}) = 0

What is the general solution for 4tan(x)-7=3tan(x)-6 ?
The general solution for 4tan(x)-7=3tan(x)-6 is x= pi/4+pin