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

The general solution for 2cos(2x)=2sin(x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin

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

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

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 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{3 π}{2} + 2 πn

sin (x) = \frac{1}{2} : x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{6} + 2 πn, x = \frac{5 π}{6} + 2 πn

- sin (θ) + 1 + cos (θ) = 0

sin (x) = \frac{1}{10}

θ, sin (θ) = 0

sec (2 z - \frac{π}{6}) = 2

2 sin (2 x) = - 1

What is the general solution for 2cos(2x)=2sin(x) ?
The general solution for 2cos(2x)=2sin(x) is x=(3pi)/2+2pin,x= pi/6+2pin,x=(5pi)/6+2pin