What is the general solution for -2sin^2(x)-cos(x)+3=0 ?

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

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-2sin^2(x)-cos(x)+3=0

- 2 sin^{2} (x) - cos (x) + 3 = 0

No Solution for x \in R

Solution steps

- 2 sin^{2} (x) - cos (x) + 3 = 0

Rewrite using trig identities

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

2 tan^{2} (2 x) - tan (2 x) = 3

sin (x) = \frac{15}{31}

4 cot (θ) - 1 = 0

x, 4 cos^{2} (x) = 5 - 4 sin (x)

cos (x) = \frac{2}{3}, - \frac{5 π}{2} < x < 2 π

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