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

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

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Popular >

2cos^2(x)+1=cos^2(x)

Solution

2 cos^{2} (x) + 1 = cos^{2} (x)

Solution

No Solution for x \in R

Solution steps

2 cos^{2} (x) + 1 = cos^{2} (x)

Solve by substitution

2 cos^{2} (x) + 1 = cos^{2} (x)

Let:

cos (x) = u

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

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

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

Move

1

to the right side

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

Subtract

1

from both sides

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

Simplify

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

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

Move

u^{2}

to the left side

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

Subtract

u^{2}

from both sides

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

Simplify

u^{2} = - 1

u^{2} = - 1

For

x^{2} = f (a)

the solutions are

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

u = - 1, u = - - 1

Simplify

- 1 : i

- 1

Apply imaginary number rule:

- 1 = i

= i

Simplify

- - 1 : - i

- - 1

Apply imaginary number rule:

- 1 = i

= - i

u = i, u = - i

Substitute back

u = cos (x)

cos (x) = i, cos (x) = - i

cos (x) = i, cos (x) = - i

cos (x) = i :

No Solution

cos (x) = i

No Solution

cos (x) = - i :

No Solution

cos (x) = - i

No Solution

Combine all the solutions

No Solution for x \in R

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Frequently Asked Questions (FAQ)

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