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

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

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

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

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

Solution steps

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

Switch sides

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

- sin (c) + cos (c) + 1 = 0

cot (a) = \frac{7}{51}

sin (x) = \frac{39}{44}

arctan (0.5) - arctan (\frac{1}{3}) = arctan (x)

arctan (x) = 3 0^{\circ}

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