What is the general solution for 4cos(x)=-sin^2(x)+1 ?

The general solution for 4cos(x)=-sin^2(x)+1 is x= pi/2+2pin,x=(3pi)/2+2pin

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4cos(x)=-sin^2(x)+1

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

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Solution steps

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

Subtract

- sin^{2} (x) + 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

cos (x) = 0, cos (x) = 4

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

cos (x) = 4 :

No Solution

Combine all the solutions

x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

sin (\frac{x}{4}) = 0

sin (\frac{4 π}{11}) = sin (θ) \cdot sin (\frac{7 π}{11})

sin (2 x) = 2 tan (2 x)

- 2 cos (2 θ) + 12 = 4 sin (θ) + 9

sec^{2} (x) + sec (x) - 2 = 0

What is the general solution for 4cos(x)=-sin^2(x)+1 ?
The general solution for 4cos(x)=-sin^2(x)+1 is x= pi/2+2pin,x=(3pi)/2+2pin