What is the general solution for -7tan(a)-14=tan(a)-6 ?

The general solution for -7tan(a)-14=tan(a)-6 is a=(3pi)/4+pin

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-7tan(a)-14=tan(a)-6

- 7 tan (a) - 14 = tan (a) - 6

a = \frac{3 π}{4} + πn

Degrees

a = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

- 7 tan (a) - 14 = tan (a) - 6

Solve by substitution

- 7 tan (a) - 14 = tan (a) - 6

Let:

tan (a) = u

- 7 u - 14 = u - 6

- 7 u - 14 = u - 6 : u = - 1

- 7 u - 14 = u - 6

Move

14

to the right side

- 7 u - 14 = u - 6

Add

14

to both sides

- 7 u - 14 + 14 = u - 6 + 14

Simplify

- 7 u = u + 8

- 7 u = u + 8

Move

u

to the left side

- 7 u = u + 8

Subtract

u

from both sides

- 7 u - u = u + 8 - u

Simplify

- 8 u = 8

- 8 u = 8

Divide both sides by

- 8

- 8 u = 8

Divide both sides by

- 8

\frac{- 8 u}{- 8} = \frac{8}{- 8}

Simplify

u = - 1

u = - 1

Substitute back

u = tan (a)

tan (a) = - 1

tan (a) = - 1

tan (a) = - 1 : a = \frac{3 π}{4} + πn

tan (a) = - 1

General solutions for

tan (a) = - 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}

a = \frac{3 π}{4} + πn

a = \frac{3 π}{4} + πn

Combine all the solutions

a = \frac{3 π}{4} + πn

cos (x) = - 0.58

tan^{4} (x) - 4 tan^{2} (x) + 3 = 0

sin (2 x) = \frac{21}{25}

cot^{2} (x) cos (x) = cot^{2} (x)

4 sin^{2} (θ) - 8 cos (θ) + 1 = 0, 0 \leq θ < 2 π

What is the general solution for -7tan(a)-14=tan(a)-6 ?
The general solution for -7tan(a)-14=tan(a)-6 is a=(3pi)/4+pin