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

The general solution for cos^2(2x)+3sin(2x)=3 is x= pi/4+pin

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

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

x = \frac{π}{4} + πn

Solution steps

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

Subtract

3

from both sides

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

Rewrite using trig identities

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

Solve by substitution

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

sin (2 x) = 1 : x = \frac{π}{4} + πn

sin (2 x) = 2 :

No Solution

Combine all the solutions

x = \frac{π}{4} + πn

- 2 cos^{2} (θ) - 4 sin (θ) + 2 = - 5 sin (θ)

t, x = cos (t) + cos (2 t)

x, sin (x) = - 1

9 - 9 sin (θ) = 6 cos^{2} (θ)

cot (2 θ) = 0

What is the general solution for cos^2(2x)+3sin(2x)=3 ?
The general solution for cos^2(2x)+3sin(2x)=3 is x= pi/4+pin