What is the general solution for csc^2(t/2)=2 ?

The general solution for csc^2(t/2)=2 is t= pi/2+4pin,t=(3pi)/2+4pin,t=(5pi)/2+4pin,t=(7pi)/2+4pin

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csc^2(t/2)=2

csc^{2} (\frac{t}{2}) = 2

t = \frac{π}{2} + 4 πn, t = \frac{3 π}{2} + 4 πn, t = \frac{5 π}{2} + 4 πn, t = \frac{7 π}{2} + 4 πn

Solution steps

csc^{2} (\frac{t}{2}) = 2

Solve by substitution

csc (\frac{t}{2}) = 2, csc (\frac{t}{2}) = - 2

csc (\frac{t}{2}) = 2 : t = \frac{π}{2} + 4 πn, t = \frac{3 π}{2} + 4 πn

csc (\frac{t}{2}) = - 2 : t = \frac{5 π}{2} + 4 πn, t = \frac{7 π}{2} + 4 πn

Combine all the solutions

t = \frac{π}{2} + 4 πn, t = \frac{3 π}{2} + 4 πn, t = \frac{5 π}{2} + 4 πn, t = \frac{7 π}{2} + 4 πn

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

- cos (3 x) = - cos (x)

2 sin (θ) cos (θ) - 2 cos (θ) = 0

4 sinh^{2} (x) = 0

- 2 cos (C) + 5 = 2 cos (C) + 4

What is the general solution for csc^2(t/2)=2 ?
The general solution for csc^2(t/2)=2 is t= pi/2+4pin,t=(3pi)/2+4pin,t=(5pi)/2+4pin,t=(7pi)/2+4pin