What is the general solution for -1/25+cos^2(x)=1 ?

The general solution for -1/25+cos^2(x)=1 is No Solution for x\in\mathbb{R}

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Popular Trigonometry >

-1/25+cos^2(x)=1

Solution

- \frac{1}{25} + cos^{2} (x) = 1

Solution

No Solution for x \in R

Solution steps

- \frac{1}{25} + cos^{2} (x) = 1

Solve by substitution

- \frac{1}{25} + cos^{2} (x) = 1

Let:

cos (x) = u

- \frac{1}{25} + u^{2} = 1

- \frac{1}{25} + u^{2} = 1 : u = \frac{26}{5}, u = - \frac{26}{5}

- \frac{1}{25} + u^{2} = 1

Move

\frac{1}{25}

to the right side

- \frac{1}{25} + u^{2} = 1

Add

\frac{1}{25}

to both sides

- \frac{1}{25} + u^{2} + \frac{1}{25} = 1 + \frac{1}{25}

Simplify

u^{2} = 1 + \frac{1}{25}

u^{2} = 1 + \frac{1}{25}

Simplify

1 + \frac{1}{25} : \frac{26}{25}

1 + \frac{1}{25}

Convert element to fraction:

1 = \frac{1 \cdot 25}{25}

= \frac{1 \cdot 25}{25} + \frac{1}{25}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 25 + 1}{25}

1 \cdot 25 + 1 = 26

1 \cdot 25 + 1

Multiply the numbers:

1 \cdot 25 = 25

= 25 + 1

Add the numbers:

25 + 1 = 26

= 26

= \frac{26}{25}

For

x^{2} = f (a)

the solutions are

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

u = \frac{26}{25}, u = - \frac{26}{25}

\frac{26}{25} = \frac{26}{5}

\frac{26}{25}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{26}{25}

25 = 5

25

Factor the number:

25 = 5^{2}

= 5^{2}

Apply radical rule:

n a^{n} = a

5^{2} = 5

= 5

= \frac{26}{5}

- \frac{26}{25} = - \frac{26}{5}

- \frac{26}{25}

Simplify

\frac{26}{25} : \frac{26}{5}

\frac{26}{25}

Apply radical rule:

n \frac{a}{b} = \frac{n a}{n b},

assuming

a \geq 0, b \geq 0

= \frac{26}{25}

25 = 5

25

Factor the number:

25 = 5^{2}

= 5^{2}

Apply radical rule:

n a^{n} = a

5^{2} = 5

= 5

= \frac{26}{5}

= - \frac{26}{5}

u = \frac{26}{5}, u = - \frac{26}{5}

Substitute back

u = cos (x)

cos (x) = \frac{26}{5}, cos (x) = - \frac{26}{5}

cos (x) = \frac{26}{5}, cos (x) = - \frac{26}{5}

cos (x) = \frac{26}{5} :

No Solution

cos (x) = \frac{26}{5}

- 1 \leq cos (x) \leq 1

No Solution

cos (x) = - \frac{26}{5} :

No Solution

cos (x) = - \frac{26}{5}

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for x \in R

Graph

Popular Examples

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Frequently Asked Questions (FAQ)

What is the general solution for -1/25+cos^2(x)=1 ?
The general solution for -1/25+cos^2(x)=1 is No Solution for x\in\mathbb{R}