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

The general solution for tan(x)(csc(x)+2)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin

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

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

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Solution steps

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

Solving each part separately

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

tan (x) = 0 : x = πn

csc (x) + 2 = 0 : x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Combine all the solutions

x = πn, x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

Since the equation is undefined for:

πn

x = \frac{7 π}{6} + 2 πn, x = \frac{11 π}{6} + 2 πn

4 cos^{2} (x) = 5 + 4 sin (x), 0 \leq x \leq 2 π

sin (π + θ) = sin (θ)

0 = 2 cos (x) + sin (x)

2 sin^{3} (x) - sin^{2} (x) - sin (x) = 0

tan (t) + sec (t) = 1

What is the general solution for tan(x)(csc(x)+2)=0 ?
The general solution for tan(x)(csc(x)+2)=0 is x=(7pi)/6+2pin,x=(11pi)/6+2pin