What is the general solution for tan^2(x)=4 ?

The general solution for tan^2(x)=4 is x=1.10714…+pin,x=-1.10714…+pin

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tan^2(x)=4

tan^{2} (x) = 4

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

Degrees

x = 63.43494 \dots^{\circ} + 18 0^{\circ} n, x = - 63.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

tan^{2} (x) = 4

Solve by substitution

tan^{2} (x) = 4

Let:

tan (x) = u

u^{2} = 4

u^{2} = 4 : u = 2, u = - 2

u^{2} = 4

For

x^{2} = f (a)

the solutions are

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

u = 4, u = - 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

- 4 = - 2

- 4

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= - 2

u = 2, u = - 2

Substitute back

u = tan (x)

tan (x) = 2, tan (x) = - 2

tan (x) = 2, tan (x) = - 2

tan (x) = 2 : x = arctan (2) + πn

tan (x) = 2

Apply trig inverse properties

tan (x) = 2

General solutions for

tan (x) = 2

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

x = arctan (2) + πn

x = arctan (2) + πn

tan (x) = - 2 : x = arctan (- 2) + πn

tan (x) = - 2

Apply trig inverse properties

tan (x) = - 2

General solutions for

tan (x) = - 2

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

x = arctan (- 2) + πn

x = arctan (- 2) + πn

Combine all the solutions

x = arctan (2) + πn, x = arctan (- 2) + πn

Show solutions in decimal form

x = 1.10714 \dots + πn, x = - 1.10714 \dots + πn

sec (x) = 3

2 cos^{2} (x) + 1 = - 3 cos (x)

8 sin (θ) + 5 = 0

2 cos^{2} (x) + 3 cos (x) = - 1, 0 \leq x \leq 2 π

9 cos (2 θ) = - 9 cos (θ)

What is the general solution for tan^2(x)=4 ?
The general solution for tan^2(x)=4 is x=1.10714…+pin,x=-1.10714…+pin