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

The general solution for -1+sin(x)+2cos^2(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = - \frac{1}{2} : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

sin (x) = 1 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn, x = \frac{π}{2} + 2 πn

3 + sin (3 x) = 2

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

sin (2 θ) = - 3 cos (2 θ)

4 sec (θ) - 4 = 0

sin (2 x) + 6 cos (x) = 0

What is the general solution for -1+sin(x)+2cos^2(x)=0 ?
The general solution for -1+sin(x)+2cos^2(x)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin,x= pi/2+2pin