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

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

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

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

x = \frac{3 π}{4} + πn

Solution steps

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

Factor

2 tan (x) csc (x) + 2 csc (x) + tan (x) + 1 : (tan (x) + 1) (2 csc (x) + 1)

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

Solving each part separately

tan (x) + 1 = 0 or 2 csc (x) + 1 = 0

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

2 csc (x) + 1 = 0 :

No Solution

Combine all the solutions

x = \frac{3 π}{4} + πn

csc (x) + cot (x) = 3, 0 \leq x \leq 2 π

(tan^{2} (x) - 4) (2 cos (x) + 1) = 0

2 sin (x) cos (x) - 3 cos (x) = 0

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

cos (a) = \frac{1}{4}

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