What is the general solution for 3cot^2(y-pi/4)=1 ?

The general solution for 3cot^2(y-pi/4)=1 is y=pin+(7pi)/(12),y=pin+(11pi)/(12)

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3cot^2(y-pi/4)=1

3 cot^{2} (y - \frac{π}{4}) = 1

y = πn + \frac{7 π}{12}, y = πn + \frac{11 π}{12}

Solution steps

3 cot^{2} (y - \frac{π}{4}) = 1

Solve by substitution

cot (y - \frac{π}{4}) = \frac{1}{3}, cot (y - \frac{π}{4}) = - \frac{1}{3}

cot (y - \frac{π}{4}) = \frac{1}{3} : y = πn + \frac{7 π}{12}

cot (y - \frac{π}{4}) = - \frac{1}{3} : y = πn + \frac{11 π}{12}

Combine all the solutions

y = πn + \frac{7 π}{12}, y = πn + \frac{11 π}{12}

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

cos (t) = - \frac{5}{13}

8 cos (x) = - 4

90 - 70 sin (x) - 130 cos (x) = 0

2 sin (x) sec (x) - 23 sin (x) = 0

What is the general solution for 3cot^2(y-pi/4)=1 ?
The general solution for 3cot^2(y-pi/4)=1 is y=pin+(7pi)/(12),y=pin+(11pi)/(12)