What is the general solution for 2tan^2(θ)-2=0 ?

The general solution for 2tan^2(θ)-2=0 is θ= pi/4+pin,θ=(3pi)/4+pin

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Popular >

2tan^2(θ)-2=0

Solution

2 tan^{2} (θ) - 2 = 0

Solution

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Degrees

θ = 4 5^{\circ} + 18 0^{\circ} n, θ = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

2 tan^{2} (θ) - 2 = 0

Solve by substitution

2 tan^{2} (θ) - 2 = 0

Let:

tan (θ) = u

2 u^{2} - 2 = 0

2 u^{2} - 2 = 0 : u = 1, u = - 1

2 u^{2} - 2 = 0

Move

2

to the right side

2 u^{2} - 2 = 0

Add

2

to both sides

2 u^{2} - 2 + 2 = 0 + 2

Simplify

2 u^{2} = 2

2 u^{2} = 2

Divide both sides by

2

2 u^{2} = 2

Divide both sides by

2

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

Simplify

u^{2} = 1

u^{2} = 1

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = 1, u = - 1

1 = 1

1

Apply rule

1 = 1

= 1

- 1 = - 1

- 1

Apply rule

1 = 1

= - 1

u = 1, u = - 1

Substitute back

u = tan (θ)

tan (θ) = 1, tan (θ) = - 1

tan (θ) = 1, tan (θ) = - 1

tan (θ) = 1 : θ = \frac{π}{4} + πn

tan (θ) = 1

General solutions for

tan (θ) = 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}

θ = \frac{π}{4} + πn

θ = \frac{π}{4} + πn

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

tan (θ) = - 1

General solutions for

tan (θ) = - 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}

θ = \frac{3 π}{4} + πn

θ = \frac{3 π}{4} + πn

Combine all the solutions

θ = \frac{π}{4} + πn, θ = \frac{3 π}{4} + πn

Popular Examples

sin^2(x)=2-sin(x)

sin^{2} (x) = 2 - sin (x)

2csc(x)cos(x)=csc(x)

2 csc (x) cos (x) = csc (x)

2cot^2(2x)=6

2 cot^{2} (2 x) = 6

-3sin(y)=0

- 3 sin (y) = 0

cos(x)= 4/9

cos (x) = \frac{4}{9}

Frequently Asked Questions (FAQ)

What is the general solution for 2tan^2(θ)-2=0 ?
The general solution for 2tan^2(θ)-2=0 is θ= pi/4+pin,θ=(3pi)/4+pin