What is the general solution for 4sec^2(x)-3=0 ?

The general solution for 4sec^2(x)-3=0 is No Solution for x\in\mathbb{R}

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Popular >

4sec^2(x)-3=0

Solution

4 sec^{2} (x) - 3 = 0

Solution

No Solution for x \in R

Solution steps

4 sec^{2} (x) - 3 = 0

Solve by substitution

4 sec^{2} (x) - 3 = 0

Let:

sec (x) = u

4 u^{2} - 3 = 0

4 u^{2} - 3 = 0 : u = \frac{3}{2}, u = - \frac{3}{2}

4 u^{2} - 3 = 0

Move

3

to the right side

4 u^{2} - 3 = 0

Add

3

to both sides

4 u^{2} - 3 + 3 = 0 + 3

Simplify

4 u^{2} = 3

4 u^{2} = 3

Divide both sides by

4

4 u^{2} = 3

Divide both sides by

4

\frac{4 u ^{2}}{4} = \frac{3}{4}

Simplify

u^{2} = \frac{3}{4}

u^{2} = \frac{3}{4}

For

x^{2} = f (a)

the solutions are

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

u = \frac{3}{4}, u = - \frac{3}{4}

\frac{3}{4} = \frac{3}{2}

\frac{3}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3}{2}

- \frac{3}{4} = - \frac{3}{2}

- \frac{3}{4}

Simplify

\frac{3}{4} : \frac{3}{2}

\frac{3}{4}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{3}{4}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{3}{2}

= - \frac{3}{2}

u = \frac{3}{2}, u = - \frac{3}{2}

Substitute back

u = sec (x)

sec (x) = \frac{3}{2}, sec (x) = - \frac{3}{2}

sec (x) = \frac{3}{2}, sec (x) = - \frac{3}{2}

sec (x) = \frac{3}{2} :

No Solution

sec (x) = \frac{3}{2}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

sec (x) = - \frac{3}{2} :

No Solution

sec (x) = - \frac{3}{2}

sec (x) \leq - 1 or sec (x) \geq 1

No Solution

Combine all the solutions

No Solution for x \in R

Popular Examples

cos^2(x)= 1/4 ,0<= x<= 2pi

cos^{2} (x) = \frac{1}{4}, 0 \leq x \leq 2 π

sin(θ)=-4/9

sin (θ) = - \frac{4}{9}

-sin(y)=0

- sin (y) = 0

0=2+4sin(θ)

0 = 2 + 4 sin (θ)

cos(x)= 71/81

cos (x) = \frac{71}{81}

Frequently Asked Questions (FAQ)

What is the general solution for 4sec^2(x)-3=0 ?
The general solution for 4sec^2(x)-3=0 is No Solution for x\in\mathbb{R}