What is the general solution for -2cos^2(x)-5sin(x)+5=0 ?

The general solution for -2cos^2(x)-5sin(x)+5=0 is x= pi/2+2pin

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

3 + 2 sin^{2} (x) - 5 sin (x) = 0

Solve by substitution

sin (x) = \frac{3}{2}, sin (x) = 1

sin (x) = \frac{3}{2} :

No Solution

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

3 - 4 sin^{3} (x) = sin^{3} (x)

cos^{4} (x) = \frac{3}{8} + \frac{1}{2} cos^{2} (x) + \frac{1}{8} cos^{4} (x)

sin (2 x) = 5 cos (x)

sin (a) = 0.4848

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

What is the general solution for -2cos^2(x)-5sin(x)+5=0 ?
The general solution for -2cos^2(x)-5sin(x)+5=0 is x= pi/2+2pin