What is the general solution for 4sin^2(x)=5-2cos(x) ?

The general solution for 4sin^2(x)=5-2cos(x) is No Solution for x\in\mathbb{R}

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4sin^2(x)=5-2cos(x)

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

No Solution for x \in R

Solution steps

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

Subtract

5 - 2 cos (x)

from both sides

4 sin^{2} (x) - 5 + 2 cos (x) = 0

Rewrite using trig identities

- 1 + 2 cos (x) - 4 cos^{2} (x) = 0

Solve by substitution

cos (x) = \frac{1}{4} - i \frac{3}{4}, cos (x) = \frac{1}{4} + i \frac{3}{4}

cos (x) = \frac{1}{4} - i \frac{3}{4} :

No Solution

cos (x) = \frac{1}{4} + i \frac{3}{4} :

No Solution

Combine all the solutions

No Solution for x \in R

sin (x + \frac{π}{6}) = - 1

sec (x) = \frac{4}{3}

4 cos (x) + 3 cos (x) = 5

4 sin (2 x) tan (x) - tan (x) = 0

3 sin (x) = 3 \cdot sin (x) + 3 cos (x) + 3 sin (x)

What is the general solution for 4sin^2(x)=5-2cos(x) ?
The general solution for 4sin^2(x)=5-2cos(x) is No Solution for x\in\mathbb{R}