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

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

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

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

No Solution for x \in R

Solution steps

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

Subtract

1 + cos (x)

from both sides

2 csc^{2} (x) - 1 - cos (x) = 0

Rewrite using trig identities

- 1 - cos (x) + \frac{2}{1 - cos ^{2} ( x )} = 0

Solve by substitution

cos (x) \approx - 1.83928 \dots

cos (x) = - 1.83928 \dots :

No Solution

Combine all the solutions

No Solution for x \in R

6 arccos (5 x) = 5 π

sin (x) + sin (x) cot (x) = 0

arctan (θ) = 1

cos (2 θ) = - \frac{1}{2}, 0 \leq θ \leq 2 π

sin (2 x) = \frac{2}{5}

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