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

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

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

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

x = 2 πn, x = π + 2 πn

Solution steps

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

Subtract

- cos^{2} (x) + 1

from both sides

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = 0, sin (x) = 4

sin (x) = 0 : x = 2 πn, x = π + 2 πn

sin (x) = 4 :

No Solution

Combine all the solutions

x = 2 πn, x = π + 2 πn

sin (2 x) = - 5 cos (2 x)

tan (x) cot (x) = sec (x) csc (x)

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

sin (θ) = 1 - cos (θ)

cos (θ) - 2 sin (θ) cos (θ) = 0

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