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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 6, sin (x) = 1

sin (x) = - 6 :

No Solution

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

- 4 + cos (4 θ) = \frac{- 8 + 3}{2}

3 cos (x) = 1 + sin (x)

6 cos^{2} (\frac{x}{2}) + cos (x) + 1 = 0

- 2 sin (θ) = 1

cos (θ) = - \frac{7}{3}

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