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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 1, sin (x) = 2

sin (x) = 1 : x = \frac{π}{2} + 2 πn

sin (x) = 2 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn

sin (2 θ) = - \frac{1}{2}, θ \geq 0

tan (x) = \frac{1}{3}, 0 \leq x \leq 2 π

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

4 sin (2 x) + 5 cos (2 x) = 0

sin (x) = cot (x)

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