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

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

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(tan^2(x)-1)(csc(x)+1)=0

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

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

Solution steps

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

Solving each part separately

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

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

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

Combine all the solutions

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

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn

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

12 sin^{2} (θ) - 3 = 0, 0 \leq θ \leq 2 π

0 = - 7.5 sin (\frac{π}{10} (t - 5)) + 8

cot (11 x + 1) = tan (6 x + 4)

2 sin (2 x) = cos (2 x + 3 0^{\circ})

tan (θ) = \frac{15}{25}

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