Question

If F(theta)=tan theta=3, find F(theta+pi)

Answer 1

Given:
f(θ) = tan(θ) = 3

Note that
$tan(x+y) = \frac{tanx + tany}{1-tanx \, tany}$

Note that tan(π) = 0.
Therefore
f(θ + π) = tan(θ+π)
            = (tanθ + tan π)/(1 -tanθ tan π)
            = 3/1 = 3

Answer: 3

Answer 2

As given 
$f(\theta) = tan( \theta) = 3$

So $f(\theta + \pi) = tan (\theta + \pi)$

And we know $tan(\theta + \pi) = -tan(\theta)$ because it is in second quadrant and tan is negative in second quadrant.

So $f(\theta + \pi) = -tan(\theta) = -3$

So answer is -3.