What is the general solution for 2cos(x/2)=sqrt(3),0<= x<= 2pi ?

The general solution for 2cos(x/2)=sqrt(3),0<= x<= 2pi is x= pi/3

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2cos(x/2)=sqrt(3),0<= x<= 2pi

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

x = \frac{π}{3}

Solution steps

2 cos (\frac{x}{2}) = 3, 0 \leq x \leq 2 π

Divide both sides by

2

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

General solutions for

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

\frac{x}{2} = \frac{π}{6} + 2 πn, \frac{x}{2} = \frac{11 π}{6} + 2 πn

Solve

\frac{x}{2} = \frac{π}{6} + 2 πn : x = \frac{π}{3} + 4 πn

Solve

\frac{x}{2} = \frac{11 π}{6} + 2 πn : x = \frac{11 π}{3} + 4 πn

x = \frac{π}{3} + 4 πn, x = \frac{11 π}{3} + 4 πn

Solutions for the range

0 \leq x \leq 2 π

x = \frac{π}{3}

sin (A) = \frac{4}{5}

3 tan^{2} (x) - 1 = 0, 0 \leq x \leq 2 π

sin (2 x) = 4 cos (x)

3 tan (2 x) - 1 = 0

cos (2 x + π) = 0

What is the general solution for 2cos(x/2)=sqrt(3),0<= x<= 2pi ?
The general solution for 2cos(x/2)=sqrt(3),0<= x<= 2pi is x= pi/3