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

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

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

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

x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - \frac{4}{3}, sin (x) = 1

sin (x) = - \frac{4}{3} :

No Solution

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{π}{2} + 2 πn

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

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

tan^{2} (b) = 3

a, sin (a + \frac{b}{2}) = cos (\frac{c}{2})

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

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