What is the general solution for 16sec^2(θ)-1=0 ?

The general solution for 16sec^2(θ)-1=0 is No Solution for θ\in\mathbb{R}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

16sec^2(θ)-1=0

Solution

16 sec^{2} (θ) - 1 = 0

Solution

No Solution for θ \in R

Solution steps

16 sec^{2} (θ) - 1 = 0

Solve by substitution

16 sec^{2} (θ) - 1 = 0

Let:

sec (θ) = u

16 u^{2} - 1 = 0

16 u^{2} - 1 = 0 : u = \frac{1}{4}, u = - \frac{1}{4}

16 u^{2} - 1 = 0

Move

1

to the right side

16 u^{2} - 1 = 0

Add

1

to both sides

16 u^{2} - 1 + 1 = 0 + 1

Simplify

16 u^{2} = 1

16 u^{2} = 1

Divide both sides by

16

16 u^{2} = 1

Divide both sides by

16

\frac{16 u ^{2}}{16} = \frac{1}{16}

Simplify

u^{2} = \frac{1}{16}

u^{2} = \frac{1}{16}

For

x^{2} = f (a)

the solutions are

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

u = \frac{1}{16}, u = - \frac{1}{16}

\frac{1}{16} = \frac{1}{4}

\frac{1}{16}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{1}{16}

16 = 4

16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

4^{2} = 4

= 4

= \frac{1}{4}

Apply rule

1 = 1

= \frac{1}{4}

- \frac{1}{16} = - \frac{1}{4}

- \frac{1}{16}

Simplify

\frac{1}{16} : \frac{1}{4}

\frac{1}{16}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{1}{16}

16 = 4

16

Factor the number:

16 = 4^{2}

= 4^{2}

Apply radical rule:

4^{2} = 4

= 4

= \frac{1}{4}

= - \frac{1}{4}

Apply rule

1 = 1

= - \frac{1}{4}

u = \frac{1}{4}, u = - \frac{1}{4}

Substitute back

u = sec (θ)

sec (θ) = \frac{1}{4}, sec (θ) = - \frac{1}{4}

sec (θ) = \frac{1}{4}, sec (θ) = - \frac{1}{4}

sec (θ) = \frac{1}{4} :

No Solution

sec (θ) = \frac{1}{4}

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

No Solution

sec (θ) = - \frac{1}{4} :

No Solution

sec (θ) = - \frac{1}{4}

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

No Solution

Combine all the solutions

No Solution for θ \in R

Popular Examples

4cos(x)-1=sqrt(5)

4 cos (x) - 1 = 5

cos(4y)=2cos(2y)-1

cos (4 y) = 2 cos (2 y) - 1

csc(x)cot(x)=2sqrt(3)

csc (x) cot (x) = 23

sin(θ)cos(θ)-sin(θ)=0

sin (θ) cos (θ) - sin (θ) = 0

cos^2(θ)+2sin(θ)+1=0

cos^{2} (θ) + 2 sin (θ) + 1 = 0

Frequently Asked Questions (FAQ)

What is the general solution for 16sec^2(θ)-1=0 ?
The general solution for 16sec^2(θ)-1=0 is No Solution for θ\in\mathbb{R}