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

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

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

3 cot^{2} (2 t - \frac{3 π}{2}) = 1

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

Solution steps

3 cot^{2} (2 t - \frac{3 π}{2}) = 1

Solve by substitution

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

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

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

Combine all the solutions

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

3 cot (θ) - 2 = 0

sin (u) = \frac{5}{13}

0.8 = cos (x)

cos (x) = \frac{12}{20}

tan (θ) = \frac{0}{1}

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