What is the general solution for 3(cos(2x)+3/2)=6 ?

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

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3(cos(2x)+3/2)=6

3 (cos (2 x) + \frac{3}{2}) = 6

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

Solution steps

3 (cos (2 x) + \frac{3}{2}) = 6

Divide both sides by

3

cos (2 x) + \frac{3}{2} = 2

Move

\frac{3}{2}

to the right side

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

General solutions for

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

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

Solve

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

Solve

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

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

sin^{2} (x) - 3 = 2 sin (x)

tan^{2} (x) - (3 + 1) tan (x) + 3 = 0

6 cos (θ) = 3

4 cos^{3} (x) = cos (x)

csc^{5} (θ) - 4 csc (θ) = 0

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