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

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

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

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

x = 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 6 :

No Solution

cos (x) = 1 : x = 2 πn

Combine all the solutions

x = 2 πn

4 sin (x) cos (x) + cos (x) = 0

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

- 2 sin^{2} (x) = 3 sin (x) + 1

cos (x) cos (2 x) + sin (x) sin (2 x) = \frac{1}{2}

2 csc^{2} (x) - 3 csc (x) - 2 = 0

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