What is the general solution for 3cos^2(θ)-10=0 ?

The general solution for 3cos^2(θ)-10=0 is No Solution for θ\in\mathbb{R}

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3cos^2(θ)-10=0

3 cos^{2} (θ) - 10 = 0

No Solution for θ \in R

Solution steps

3 cos^{2} (θ) - 10 = 0

Solve by substitution

3 cos^{2} (θ) - 10 = 0

Let:

cos (θ) = u

3 u^{2} - 10 = 0

3 u^{2} - 10 = 0 : u = \frac{10}{3}, u = - \frac{10}{3}

3 u^{2} - 10 = 0

Move

10

to the right side

3 u^{2} - 10 = 0

Add

10

to both sides

3 u^{2} - 10 + 10 = 0 + 10

Simplify

3 u^{2} = 10

3 u^{2} = 10

Divide both sides by

3

3 u^{2} = 10

Divide both sides by

3

\frac{3 u ^{2}}{3} = \frac{10}{3}

Simplify

u^{2} = \frac{10}{3}

u^{2} = \frac{10}{3}

For

x^{2} = f (a)

the solutions are

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

u = \frac{10}{3}, u = - \frac{10}{3}

Substitute back

u = cos (θ)

cos (θ) = \frac{10}{3}, cos (θ) = - \frac{10}{3}

cos (θ) = \frac{10}{3}, cos (θ) = - \frac{10}{3}

cos (θ) = \frac{10}{3} :

No Solution

cos (θ) = \frac{10}{3}

- 1 \leq cos (x) \leq 1

No Solution

cos (θ) = - \frac{10}{3} :

No Solution

cos (θ) = - \frac{10}{3}

- 1 \leq cos (x) \leq 1

No Solution

Combine all the solutions

No Solution for θ \in R

\frac{sin ( x ) + cos ( x )}{sin ( x )} = 1 \frac{1}{tan ( x )}

arctan (x) = \frac{- π}{2}

cot (θ) = - 3, sin (2 θ)

3 sin (2 x) - 1 cos (x) = 0

sin (4 x - 3) = cos (5 x - 6)

What is the general solution for 3cos^2(θ)-10=0 ?
The general solution for 3cos^2(θ)-10=0 is No Solution for θ\in\mathbb{R}