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

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

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-cos(2x)=sin(x)

- cos (2 x) = sin (x)

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

Solution steps

- cos (2 x) = sin (x)

Subtract

sin (x)

from both sides

- cos (2 x) - sin (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 tan^{2} (x) - sec^{2} (x) = 0

2 cos (x - \frac{π}{3}) = 3

tan^{2} (x) - 5 tan (x) + 5 = 0

4 sin^{2} (\frac{x}{2}) + cos^{2} (x) = 2

2 cos^{2} (x) - 2 cos (2 x) = 1

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