What is the general solution for 1-3cos(x)=sin^2(x) ?

The general solution for 1-3cos(x)=sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin

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1-3cos(x)=sin^2(x)

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

sin^{2} (x)

from both sides

1 - 3 cos (x) - sin^{2} (x) = 0

Rewrite using trig identities

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

Solve by substitution

cos (x) = 3, cos (x) = 0

cos (x) = 3 :

No Solution

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

15 sec^{2} (x) - 20 = 0

1 - 2 tan^{2} (x) = - tan^{2} (x)

sin (x) = - \frac{1}{2}, 0 \leq x \leq 2 π

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

sin^{2} (a) sec (a) = tan^{2} (a)

What is the general solution for 1-3cos(x)=sin^2(x) ?
The general solution for 1-3cos(x)=sin^2(x) is x= pi/2+2pin,x=(3pi)/2+2pin