What is the general solution for cos(x)-2cos^2(x)-1=0 ?

The general solution for cos(x)-2cos^2(x)-1=0 is No Solution for x\in\mathbb{R}

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cos(x)-2cos^2(x)-1=0

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

No Solution for x \in R

Solution steps

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

Solve by substitution

cos (x) = \frac{1}{4} - i \frac{7}{4}, cos (x) = \frac{1}{4} + i \frac{7}{4}

cos (x) = \frac{1}{4} - i \frac{7}{4} :

No Solution

cos (x) = \frac{1}{4} + i \frac{7}{4} :

No Solution

Combine all the solutions

No Solution for x \in R

cos (2 x) = \frac{2}{3}

- cos (7 x) + cos (3 x) = sin (5 x)

2 sin (θ) - 3 csc (θ) + 5 = 0

csc^{4} (2 x) - 4 = 0

sin (θ) = \frac{4}{13}

What is the general solution for cos(x)-2cos^2(x)-1=0 ?
The general solution for cos(x)-2cos^2(x)-1=0 is No Solution for x\in\mathbb{R}