What is the general solution for cot^2(x)csc^2(x)+2csc^2(x)-cot^2(x)=2 ?

The general solution for cot^2(x)csc^2(x)+2csc^2(x)-cot^2(x)=2 is x=(3pi)/2+2pin,x= pi/2+2pin

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cot^2(x)csc^2(x)+2csc^2(x)-cot^2(x)=2

cot^{2} (x) csc^{2} (x) + 2 csc^{2} (x) - cot^{2} (x) = 2

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

Solution steps

cot^{2} (x) csc^{2} (x) + 2 csc^{2} (x) - cot^{2} (x) = 2

Subtract

2

from both sides

cot^{2} (x) csc^{2} (x) + 2 csc^{2} (x) - cot^{2} (x) - 2 = 0

Factor

cot^{2} (x) csc^{2} (x) + 2 csc^{2} (x) - cot^{2} (x) - 2 : (cot^{2} (x) + 2) (csc (x) + 1) (csc (x) - 1)

(cot^{2} (x) + 2) (csc (x) + 1) (csc (x) - 1) = 0

Solving each part separately

cot^{2} (x) + 2 = 0 or csc (x) + 1 = 0 or csc (x) - 1 = 0

cot^{2} (x) + 2 = 0 :

No Solution

csc (x) + 1 = 0 : x = \frac{3 π}{2} + 2 πn

csc (x) - 1 = 0 : x = \frac{π}{2} + 2 πn

Combine all the solutions

x = \frac{3 π}{2} + 2 πn, x = \frac{π}{2} + 2 πn

cos (t) = \frac{3}{5}, 0 < t < \frac{π}{2}

cos (x) = \frac{- 2}{2}

y, - ln (cos (x)) = - 2 cos (x) \cdot sin (y)

2 sin (a) + csc (a) = 3

cos (x) = \frac{- 2}{7}

What is the general solution for cot^2(x)csc^2(x)+2csc^2(x)-cot^2(x)=2 ?
The general solution for cot^2(x)csc^2(x)+2csc^2(x)-cot^2(x)=2 is x=(3pi)/2+2pin,x= pi/2+2pin