What is the general solution for cos^2(60)+cos^2(45)+cos^2(x)=1 ?

The general solution for cos^2(60)+cos^2(45)+cos^2(x)=1 is No Solution for x\in\mathbb{R}

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Popular >

cos^2(60)+cos^2(45)+cos^2(x)=1

Solution

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

Solution

No Solution for x \in R

Solution steps

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

Solve by substitution

cos^{2} (60) + cos^{2} (45) + cos^{2} (x) = 1

Let:

cos (x) = u

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

cos^{2} (60) + cos^{2} (45) + u^{2} = 1 : u = i - 1 + cos^{2} (60) + cos^{2} (45), u = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

Move

cos^{2} (60)

to the right side

cos^{2} (60) + cos^{2} (45) + u^{2} = 1

Subtract

cos^{2} (60)

from both sides

cos^{2} (60) + cos^{2} (45) + u^{2} - cos^{2} (60) = 1 - cos^{2} (60)

Simplify

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

Move

cos^{2} (45)

to the right side

cos^{2} (45) + u^{2} = 1 - cos^{2} (60)

Subtract

cos^{2} (45)

from both sides

cos^{2} (45) + u^{2} - cos^{2} (45) = 1 - cos^{2} (60) - cos^{2} (45)

Simplify

u^{2} = 1 - cos^{2} (60) - cos^{2} (45)

u^{2} = 1 - cos^{2} (60) - cos^{2} (45)

For

x^{2} = f (a)

the solutions are

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

u = 1 - cos^{2} (60) - cos^{2} (45), u = - 1 - cos^{2} (60) - cos^{2} (45)

Simplify

1 - cos^{2} (60) - cos^{2} (45) : i - 1 + cos^{2} (60) + cos^{2} (45)

1 - cos^{2} (60) - cos^{2} (45)

Apply imaginary number rule:

- a = i a

= i cos^{2} (60) + cos^{2} (45) - 1

Simplify

- 1 - cos^{2} (60) - cos^{2} (45) : - i - 1 + cos^{2} (60) + cos^{2} (45)

- 1 - cos^{2} (60) - cos^{2} (45)

Apply imaginary number rule:

- a = i a

= - i cos^{2} (60) + cos^{2} (45) - 1

u = i - 1 + cos^{2} (60) + cos^{2} (45), u = - i - 1 + cos^{2} (60) + cos^{2} (45)

Substitute back

u = cos (x)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45), cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45), cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45) :

No Solution

cos (x) = i - 1 + cos^{2} (60) + cos^{2} (45)

No Solution

cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45) :

No Solution

cos (x) = - i - 1 + cos^{2} (60) + cos^{2} (45)

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 cos^2(60)+cos^2(45)+cos^2(x)=1 ?
The general solution for cos^2(60)+cos^2(45)+cos^2(x)=1 is No Solution for x\in\mathbb{R}