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

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

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

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

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

Solution steps

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

Rewrite using trig identities

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

Solve by substitution

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

sin (x) = 1 : x = \frac{π}{2} + 2 πn

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

Combine all the solutions

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

- 2 cos (B) + 4 = cos (B) + 6

4 - 2 sin^{2} (x) = - sin (x) + 3

csc^{3} (x) + csc^{2} (x) = 2 csc (x) + 2

cot^{2} (x) sin (x) = cot^{2} (x)

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

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