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

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

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

solve for

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

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

Solution steps

cos (2 x) + sin (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

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

cos (\frac{x}{4}) = \frac{1}{2}

cos (2 x) = 5 cos (x) - 3

4 tan (A) = 2 tan (A) - 2

2 sin (θ) = tan (θ)

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