What is the general solution for 4cos(x)=-sin^2(x)+4 ?

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

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4cos(x)=-sin^2(x)+4

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

x = 2 πn

Solution steps

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

Subtract

- sin^{2} (x) + 4

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 1, cos (x) = 3

cos (x) = 1 : x = 2 πn

cos (x) = 3 :

No Solution

Combine all the solutions

x = 2 πn

7 cos^{2} (θ) + 5 = 2 sin (θ) + 7

1 - cos (2 x) = 1 + cos (2 x)

5 cos^{2} (x) - 10 cos (x) + 5 = 0

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

8 tan (b) + 12 = 3 tan (b) + 7

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