What is the general solution for 3cos(2x)=3sin(x) ?

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

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

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

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

Solution steps

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

Subtract

3 sin (x)

from both sides

3 cos (2 x) - 3 sin (x) = 0

Rewrite using trig identities

(1 - 2 sin^{2} (x)) \cdot 3 - 3 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

4 cos (\frac{θ}{2}) + 3 = - 2 cos (θ)

8 cos (2 x) - 1 = 2

2 cos (2 x) + 3 = 23

sin (x) cos (2 x) = \frac{1}{2} (1 + sin (x))

e^{s i n (x)} = 2

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