What is the general solution for 3cos^2(x)=9sin(x)+9 ?

The general solution for 3cos^2(x)=9sin(x)+9 is x=(3pi)/2+2pin

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3cos^2(x)=9sin(x)+9

3 cos^{2} (x) = 9 sin (x) + 9

x = \frac{3 π}{2} + 2 πn

Solution steps

3 cos^{2} (x) = 9 sin (x) + 9

Subtract

9 sin (x) + 9

from both sides

3 cos^{2} (x) - 9 sin (x) - 9 = 0

Rewrite using trig identities

- 6 - 3 sin^{2} (x) - 9 sin (x) = 0

Solve by substitution

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

sin (x) = - 2 :

No Solution

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

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

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

2 sin^{2} (x) = 1, + [0, + 2 π]

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

sin (x) = \frac{33}{80}

What is the general solution for 3cos^2(x)=9sin(x)+9 ?
The general solution for 3cos^2(x)=9sin(x)+9 is x=(3pi)/2+2pin