What is the general solution for cos((2x+3)/2)=-1/2 ?

The general solution for cos((2x+3)/2)=-1/2 is x=2pin-3/2+(2pi)/3 ,x=2pin-3/2+(4pi)/3

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cos((2x+3)/2)=-1/2

cos (\frac{2 x + 3}{2}) = - \frac{1}{2}

x = 2 πn - \frac{3}{2} + \frac{2 π}{3}, x = 2 πn - \frac{3}{2} + \frac{4 π}{3}

Solution steps

cos (\frac{2 x + 3}{2}) = - \frac{1}{2}

General solutions for

cos (\frac{2 x + 3}{2}) = - \frac{1}{2}

\frac{2 x + 3}{2} = \frac{2 π}{3} + 2 πn, \frac{2 x + 3}{2} = \frac{4 π}{3} + 2 πn

Solve

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

Solve

\frac{2 x + 3}{2} = \frac{4 π}{3} + 2 πn : x = 2 πn - \frac{3}{2} + \frac{4 π}{3}

x = 2 πn - \frac{3}{2} + \frac{2 π}{3}, x = 2 πn - \frac{3}{2} + \frac{4 π}{3}

1 = cot^{2} (x) + csc (x)

sin (\frac{θ}{2}) = \frac{3}{2}

cos (θ) = - 2

cos (x) = - \frac{π}{3}

tan (θ) = - 2 sin (θ)

What is the general solution for cos((2x+3)/2)=-1/2 ?
The general solution for cos((2x+3)/2)=-1/2 is x=2pin-3/2+(2pi)/3 ,x=2pin-3/2+(4pi)/3