What is the general solution for 3cot^2(2x-(3pi)/2)=1 ?

The general solution for 3cot^2(2x-(3pi)/2)=1 is x=(pin)/2+(11pi}{12},x=(pin)/2+\frac{13pi)/(12)

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3cot^2(2x-(3pi)/2)=1

3 cot^{2} (2 x - \frac{3 π}{2}) = 1

x = \frac{πn}{2} + \frac{11 π}{12}, x = \frac{πn}{2} + \frac{13 π}{12}

Solution steps

3 cot^{2} (2 x - \frac{3 π}{2}) = 1

Solve by substitution

cot (2 x - \frac{3 π}{2}) = \frac{1}{3}, cot (2 x - \frac{3 π}{2}) = - \frac{1}{3}

cot (2 x - \frac{3 π}{2}) = \frac{1}{3} : x = \frac{πn}{2} + \frac{11 π}{12}

cot (2 x - \frac{3 π}{2}) = - \frac{1}{3} : x = \frac{πn}{2} + \frac{13 π}{12}

Combine all the solutions

x = \frac{πn}{2} + \frac{11 π}{12}, x = \frac{πn}{2} + \frac{13 π}{12}

1.6 sin (θ) = 1.49

cos (x) = 0.695

3 + sec (x) = 5

cos (x) = \frac{3}{30}

- 5 sin (t) + 9 cos (t) = 0

What is the general solution for 3cot^2(2x-(3pi)/2)=1 ?
The general solution for 3cot^2(2x-(3pi)/2)=1 is x=(pin)/2+(11pi}{12},x=(pin)/2+\frac{13pi)/(12)