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

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

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

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

x = π + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

cos (x) = - 1 : x = π + 2 πn

cos (x) = 3 :

No Solution

Combine all the solutions

x = π + 2 πn

6 sin^{2} (x) - 5 cos (x) - 2 = 0

sin (θ) + cos (θ) = \frac{3}{5}

sec (x) - 4 = 0

csc (θ) - cot^{2} (θ) + 1 = 0

sin (x - 4 0^{\circ}) = 1

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