What is the general solution for sin^2(x)+cos(x)+1=0 ?

The general solution for sin^2(x)+cos(x)+1=0 is x=pi+2pin

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sin^2(x)+cos(x)+1=0

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

x = π + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = 2 :

No Solution

Combine all the solutions

x = π + 2 πn

2 cos (2 x) = 0

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

sec (x) = - 1

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

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

What is the general solution for sin^2(x)+cos(x)+1=0 ?
The general solution for sin^2(x)+cos(x)+1=0 is x=pi+2pin