What is the general solution for sin^2(x)-3cos(x)-1=0 ?

The general solution for sin^2(x)-3cos(x)-1=0 is x= pi/2+2pin,x=(3pi)/2+2pin

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

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

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

Solution steps

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

2 cos^{2} (θ) + 2 cos (θ) = 0

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

cos (2 x) + 5 sin (x) + 2 = 0, 0 \leq x \leq 2 π

2 cos (4 θ) - 1 = 0

3 cos (x) = 8 tan (x)

What is the general solution for sin^2(x)-3cos(x)-1=0 ?
The general solution for sin^2(x)-3cos(x)-1=0 is x= pi/2+2pin,x=(3pi)/2+2pin