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

cot (x) cos^{2} (x) = 2 cot (x), 0 \leq x \leq 2 π

2 cot^{2} (3 θ) = 5 csc (3 θ) - 4

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

1 = 2 sin (2 θ)

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

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}