What is the general solution for 25csc^2(θ)-4=0 ?

The general solution for 25csc^2(θ)-4=0 is No Solution for θ\in\mathbb{R}

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Popular >

25csc^2(θ)-4=0

Solution

25 csc^{2} (θ) - 4 = 0

Solution

No Solution for θ \in R

Solution steps

25 csc^{2} (θ) - 4 = 0

Solve by substitution

25 csc^{2} (θ) - 4 = 0

Let:

csc (θ) = u

25 u^{2} - 4 = 0

25 u^{2} - 4 = 0 : u = \frac{2}{5}, u = - \frac{2}{5}

25 u^{2} - 4 = 0

Move

4

to the right side

25 u^{2} - 4 = 0

Add

4

to both sides

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

Simplify

25 u^{2} = 4

25 u^{2} = 4

Divide both sides by

25

25 u^{2} = 4

Divide both sides by

25

\frac{25 u ^{2}}{25} = \frac{4}{25}

Simplify

u^{2} = \frac{4}{25}

u^{2} = \frac{4}{25}

For

x^{2} = f (a)

the solutions are

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

u = \frac{4}{25}, u = - \frac{4}{25}

\frac{4}{25} = \frac{2}{5}

\frac{4}{25}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

Factor the number:

25 = 5^{2}

= 5^{2}

Apply radical rule:

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{5}

- \frac{4}{25} = - \frac{2}{5}

- \frac{4}{25}

Simplify

\frac{4}{25} : \frac{2}{5}

\frac{4}{25}

Apply radical rule:

assuming

a \geq 0, b \geq 0

= \frac{4}{25}

25 = 5

25

Factor the number:

25 = 5^{2}

= 5^{2}

Apply radical rule:

5^{2} = 5

= 5

= \frac{4}{5}

4 = 2

4

Factor the number:

4 = 2^{2}

= 2^{2}

Apply radical rule:

2^{2} = 2

= 2

= \frac{2}{5}

= - \frac{2}{5}

u = \frac{2}{5}, u = - \frac{2}{5}

Substitute back

u = csc (θ)

csc (θ) = \frac{2}{5}, csc (θ) = - \frac{2}{5}

csc (θ) = \frac{2}{5}, csc (θ) = - \frac{2}{5}

csc (θ) = \frac{2}{5} :

No Solution

csc (θ) = \frac{2}{5}

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

No Solution

csc (θ) = - \frac{2}{5} :

No Solution

csc (θ) = - \frac{2}{5}

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

No Solution

Combine all the solutions

No Solution for θ \in R

Popular Examples

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tan (θ) = \frac{1}{5}

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3 cos (x) - 3 sin (x) = 0

sin^3(x)=3sin(x)-4sin^3(x)

sin^{3} (x) = 3 sin (x) - 4 sin^{3} (x)

Frequently Asked Questions (FAQ)

What is the general solution for 25csc^2(θ)-4=0 ?
The general solution for 25csc^2(θ)-4=0 is No Solution for θ\in\mathbb{R}