What is the general solution for (2sin^2(x)-1)(tan(x)-1)=0 ?

The general solution for (2sin^2(x)-1)(tan(x)-1)=0 is x=(3pi)/4+2pin,x=(7pi)/4+2pin,x= pi/4+pin

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(2sin^2(x)-1)(tan(x)-1)=0

(2 sin^{2} (x) - 1) (tan (x) - 1) = 0

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

Solution steps

(2 sin^{2} (x) - 1) (tan (x) - 1) = 0

Solving each part separately

2 sin^{2} (x) - 1 = 0 or tan (x) - 1 = 0

2 sin^{2} (x) - 1 = 0 : x = \frac{π}{4} + 2 πn, x = \frac{3 π}{4} + 2 πn, x = \frac{5 π}{4} + 2 πn, x = \frac{7 π}{4} + 2 πn

tan (x) - 1 = 0 : x = \frac{π}{4} + πn

Combine all the solutions

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

Merge Overlapping Intervals

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

(csc (x) + 2) (csc (x) - 2) = 0, 0 \leq x \leq 2 π

cos (x) = 55

cos (x) = 35

sin (x) = \frac{12}{10}

cos (x) = 45

What is the general solution for (2sin^2(x)-1)(tan(x)-1)=0 ?
The general solution for (2sin^2(x)-1)(tan(x)-1)=0 is x=(3pi)/4+2pin,x=(7pi)/4+2pin,x= pi/4+pin