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

The general solution for 2cos(2x-pi/2)=sqrt(3) is x=pin+pi/3 ,x=pin+(7pi)/6

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2cos(2x-pi/2)=sqrt(3)

2 cos (2 x - \frac{π}{2}) = 3

x = πn + \frac{π}{3}, x = πn + \frac{7 π}{6}

Solution steps

2 cos (2 x - \frac{π}{2}) = 3

Divide both sides by

2

cos (2 x - \frac{π}{2}) = \frac{3}{2}

General solutions for

cos (2 x - \frac{π}{2}) = \frac{3}{2}

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

Solve

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

Solve

2 x - \frac{π}{2} = \frac{11 π}{6} + 2 πn : x = πn + \frac{7 π}{6}

x = πn + \frac{π}{3}, x = πn + \frac{7 π}{6}

cos (2 x) - 2 sin^{2} (x) = 0

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

2 cos (t) + 1 = 0

sin (3 x) = \frac{1}{2}

tan^{2} (θ) = - tan (θ)

What is the general solution for 2cos(2x-pi/2)=sqrt(3) ?
The general solution for 2cos(2x-pi/2)=sqrt(3) is x=pin+pi/3 ,x=pin+(7pi)/6