What is the general solution for tan^2(x)-9=0 ?

The general solution for tan^2(x)-9=0 is x=1.24904…+pin,x=-1.24904…+pin

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tan^2(x)-9=0

tan^{2} (x) - 9 = 0

x = 1.24904 \dots + πn, x = - 1.24904 \dots + πn

Degrees

x = 71.56505 \dots^{\circ} + 18 0^{\circ} n, x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan^{2} (x) - 9 = 0

Solve by substitution

tan^{2} (x) - 9 = 0

Let:

tan (x) = u

u^{2} - 9 = 0

u^{2} - 9 = 0 : u = 3, u = - 3

u^{2} - 9 = 0

Move

9

to the right side

u^{2} - 9 = 0

Add

9

to both sides

u^{2} - 9 + 9 = 0 + 9

Simplify

u^{2} = 9

u^{2} = 9

For

x^{2} = f (a)

the solutions are

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

u = 9, u = - 9

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

- 9 = - 3

- 9

9 = 3

9

Factor the number:

9 = 3^{2}

= 3^{2}

Apply radical rule:

3^{2} = 3

= 3

= - 3

u = 3, u = - 3

Substitute back

u = tan (x)

tan (x) = 3, tan (x) = - 3

tan (x) = 3, tan (x) = - 3

tan (x) = 3 : x = arctan (3) + πn

tan (x) = 3

Apply trig inverse properties

tan (x) = 3

General solutions for

tan (x) = 3

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (3) + πn

x = arctan (3) + πn

tan (x) = - 3 : x = arctan (- 3) + πn

tan (x) = - 3

Apply trig inverse properties

tan (x) = - 3

General solutions for

tan (x) = - 3

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 3) + πn

x = arctan (- 3) + πn

Combine all the solutions

x = arctan (3) + πn, x = arctan (- 3) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn, x = - 1.24904 \dots + πn

2 = - 4 - 3 csc (θ)

x, 3 tan (2 x) = - 1

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

2 sin^{2} (x) + 4 cos^{2} (x) = 1

- sin (θ) = \frac{n}{2} - 3

What is the general solution for tan^2(x)-9=0 ?
The general solution for tan^2(x)-9=0 is x=1.24904…+pin,x=-1.24904…+pin