What is the general solution for 1/2 cos(x/2)=0 ?

The general solution for 1/2 cos(x/2)=0 is x=pi+4pin,x=3pi+4pin

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1/2 cos(x/2)=0

\frac{1}{2} cos (\frac{x}{2}) = 0

x = π + 4 πn, x = 3 π + 4 πn

Solution steps

\frac{1}{2} cos (\frac{x}{2}) = 0

Multiply both sides by

2

cos (\frac{x}{2}) = 0

General solutions for

cos (\frac{x}{2}) = 0

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

Solve

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

Solve

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

x = π + 4 πn, x = 3 π + 4 πn

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

tan (\frac{θ}{2}) = 3

tan (x) = \frac{1}{4}

cos^{2} (θ) - sin^{2} (θ) + sin (θ) = 0

3 tan (2 x) + 1 = 0

What is the general solution for 1/2 cos(x/2)=0 ?
The general solution for 1/2 cos(x/2)=0 is x=pi+4pin,x=3pi+4pin