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

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

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

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

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

Solution steps

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

Subtract

2 sin (x)

from both sides

- 2 cos (2 x) - 2 sin (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 (θ) - 0.2 cos (θ) = \frac{7.51}{9.8}

23 = - 6 tan (θ)

- 3 - \frac{5}{2} \cdot cos (θ) = - 3 - 3 cos (θ)

tan (θ) = - \frac{6}{5}

3 sec (2 θ) = - 18

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