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

The general solution for cos(2x)+sin(x)+2=0 is x=(3pi)/2+2pin

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

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

x = \frac{3 π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

sin (x) = - 1, sin (x) = \frac{3}{2}

sin (x) = - 1 : x = \frac{3 π}{2} + 2 πn

sin (x) = \frac{3}{2} :

No Solution

Combine all the solutions

x = \frac{3 π}{2} + 2 πn

3 tan (x) = - 1

9 cot^{2} (x) - 3 = 0

3 cos (x) - 4 sin (x) = 0

sec^{2} (x) - 4 sec (x) = 0

sin (x) = \frac{5}{8}

What is the general solution for cos(2x)+sin(x)+2=0 ?
The general solution for cos(2x)+sin(x)+2=0 is x=(3pi)/2+2pin