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

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

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tan(x)cos(x)=0

tan (x) cos (x) = 0

x = πn

Solution steps

tan (x) cos (x) = 0

Solving each part separately

tan (x) = 0 or cos (x) = 0

tan (x) = 0 : x = πn

cos (x) = 0 : x = \frac{π}{2} + 2 πn, x = \frac{3 π}{2} + 2 πn

Combine all the solutions

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

Since the equation is undefined for:

\frac{π}{2} + 2 πn, \frac{3 π}{2} + 2 πn

x = πn

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

2 csc^{2} (x) - 2 csc (x) - 2 = 0

sin (t) = - \frac{2}{2}

9 cos (2 θ) = 9 cos^{2} (θ) - 4

- 10 sin (x) = 0

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