What is the general solution for (tan(a)+1)/(tan(a))=2 ?

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

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(tan(a)+1)/(tan(a))=2

Solution

\frac{tan ( a ) + 1}{tan ( a )} = 2

Solution

a = \frac{π}{4} + πn

Degrees

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

Solution steps

\frac{tan ( a ) + 1}{tan ( a )} = 2

Solve by substitution

\frac{tan ( a ) + 1}{tan ( a )} = 2

Let:

tan (a) = u

\frac{u + 1}{u} = 2

\frac{u + 1}{u} = 2 : u = 1

\frac{u + 1}{u} = 2

Multiply both sides by

u

\frac{u + 1}{u} = 2

Multiply both sides by

u

\frac{u + 1}{u} u = 2 u

Simplify

u + 1 = 2 u

u + 1 = 2 u

Move

1

to the right side

u + 1 = 2 u

Subtract

1

from both sides

u + 1 - 1 = 2 u - 1

Simplify

u = 2 u - 1

u = 2 u - 1

Move

2 u

to the left side

u = 2 u - 1

Subtract

2 u

from both sides

u - 2 u = 2 u - 1 - 2 u

Simplify

- u = - 1

- u = - 1

Divide both sides by

- 1

- u = - 1

Divide both sides by

- 1

\frac{- u}{- 1} = \frac{- 1}{- 1}

Simplify

u = 1

u = 1

Verify Solutions

Find undefined (singularity) points:

u = 0

Take the denominator(s) of

\frac{u + 1}{u}

and compare to zero

u = 0

The following points are undefined

u = 0

Combine undefined points with solutions:

u = 1

Substitute back

u = tan (a)

tan (a) = 1

tan (a) = 1

tan (a) = 1 : a = \frac{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{π}{4} + πn

a = \frac{π}{4} + πn

Combine all the solutions

a = \frac{π}{4} + πn

Popular Examples

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2sec(2x)+tan(2x)-3=0

2 sec (2 x) + tan (2 x) - 3 = 0

solvefor x,5=9.4cos(x)solve for

x, 5 = 9.4 cos (x)

20=2.891sin(0.016d-1.183)+18.512

20 = 2.891 sin (0.016 d - 1.183) + 18.512

2sin(θ)=-1,0<= θ<2pi

2 sin (θ) = - 1, 0 \leq θ < 2 π

Frequently Asked Questions (FAQ)

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