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

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

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-sin(x)=cos(2x)

- sin (x) = 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

- sin (x) = cos (2 x)

Subtract

cos (2 x)

from both sides

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

Rewrite using trig identities

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

- 6 sin (x) - 6 cos (x) = 0

sin (4 x) - sin (2 x) = cos (3 x)

sin (x) = 0.7392

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

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