What is tan(θ)+tan(θ+pi)+tan(θ+2pi) ?

The solution to tan(θ)+tan(θ+pi)+tan(θ+2pi) is 3tan(θ)

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simplify tan(θ)+tan(θ+pi)+tan(θ+2pi)

simplify

tan (θ) + tan (θ + π) + tan (θ + 2 π)

3 tan (θ)

Solution steps

tan (θ) + tan (θ + π) + tan (θ + 2 π)

Rewrite using trig identities

= tan (θ) + \frac{sin ( θ )}{cos ( θ )} + tan (θ + 2 π)

Rewrite using trig identities

= tan (θ) + \frac{sin ( θ )}{cos ( θ )} + \frac{sin ( θ )}{cos ( θ )}

Combine the fractions

\frac{sin ( θ )}{cos ( θ )} + \frac{sin ( θ )}{cos ( θ )} : \frac{2 sin ( θ )}{cos ( θ )}

= tan (θ) + \frac{2 sin ( θ )}{cos ( θ )}

Rewrite using trig identities

= 3 tan (θ)

a csc (- 1)

cos (3 x + \frac{π}{2})

tan (x + \frac{5 π}{4})

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cot^{2} (x) sec (x) - cos (x)

What is tan(θ)+tan(θ+pi)+tan(θ+2pi) ?
The solution to tan(θ)+tan(θ+pi)+tan(θ+2pi) is 3tan(θ)