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

The general solution for tan(x)sin(x)+tan(x)=0 is x=pin

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tan(x)sin(x)+tan(x)=0

tan (x) sin (x) + tan (x) = 0

x = πn

Solution steps

tan (x) sin (x) + tan (x) = 0

Factor

tan (x) sin (x) + tan (x) : tan (x) (sin (x) + 1)

tan (x) (sin (x) + 1) = 0

Solving each part separately

tan (x) = 0 or sin (x) + 1 = 0

tan (x) = 0 : x = πn

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

Combine all the solutions

x = πn, x = \frac{3 π}{2} + 2 πn

Since the equation is undefined for:

\frac{3 π}{2} + 2 πn

x = πn

y, tan (x y) = x

cot^{2} (x) - 3 csc (x) + 3 = 0

2 sin^{2} (\frac{θ}{2} - \frac{π}{6}) - 1 = 0

cos^{2} (3 6^{\circ}) - sin^{2} (3 6^{\circ}) = cos (x)

23 cos (x) = - 17 - cos (x)

What is the general solution for tan(x)sin(x)+tan(x)=0 ?
The general solution for tan(x)sin(x)+tan(x)=0 is x=pin