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

The general solution for 2cos^2(x)=4-5sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Solution steps

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

Subtract

4 - 5 sin (x)

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = \frac{1}{2}, sin (x) = 2

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

sin (x) = 2 :

No Solution

Combine all the solutions

x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

2 csc (2 x) + 2 = 0

x, cos (x) = - sin (x)

csc (x) - 2 sin (x) = 0

sin (2 x + 11 0^{\circ}) + sin (2 x - 1 0^{\circ}) = \frac{1}{2}

6 cot^{2} (x) - 18 = 0

What is the general solution for 2cos^2(x)=4-5sin(x) ?
The general solution for 2cos^2(x)=4-5sin(x) is x= pi/6+2pin,x=(5pi)/6+2pin