What is the general solution for sec^2(x)+3=1 ?

The general solution for sec^2(x)+3=1 is No Solution for x\in\mathbb{R}

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sec^2(x)+3=1

sec^{2} (x) + 3 = 1

No Solution for x \in R

Solution steps

sec^{2} (x) + 3 = 1

Solve by substitution

sec^{2} (x) + 3 = 1

Let:

sec (x) = u

u^{2} + 3 = 1

u^{2} + 3 = 1 : u = 2 i, u = - 2 i

u^{2} + 3 = 1

Move

3

to the right side

u^{2} + 3 = 1

Subtract

3

from both sides

u^{2} + 3 - 3 = 1 - 3

Simplify

u^{2} = - 2

u^{2} = - 2

For

x^{2} = f (a)

the solutions are

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

u = - 2, u = - - 2

Simplify

- 2 : 2 i

- 2

Apply radical rule:

- a = - 1 a

- 2 = - 1 2

= - 1 2

Apply imaginary number rule:

- 1 = i

= 2 i

Simplify

- - 2 : - 2 i

- - 2

Simplify

- 2 : 2 i

- 2

Apply radical rule:

- a = - 1 a

- 2 = - 1 2

= - 1 2

Apply imaginary number rule:

- 1 = i

= 2 i

= - 2 i

u = 2 i, u = - 2 i

Substitute back

u = sec (x)

sec (x) = 2 i, sec (x) = - 2 i

sec (x) = 2 i, sec (x) = - 2 i

sec (x) = 2 i :

No Solution

sec (x) = 2 i

No Solution

sec (x) = - 2 i :

No Solution

sec (x) = - 2 i

No Solution

Combine all the solutions

No Solution for x \in R

cot (θ) + tan (θ) = 0

cot (θ) + tan (θ) = 1

sec (θ) = \frac{1}{2}

sin (2 x) = sin (4 8^{\circ})

sin (\frac{1}{5} x) = 0

What is the general solution for sec^2(x)+3=1 ?
The general solution for sec^2(x)+3=1 is No Solution for x\in\mathbb{R}