tan(x + 450 degrees)

I only have a moment right now, but one thing I notice immediately, is that 450 degrees has the same trigonometric functions as 450 - 360 = 90 degrees. The tangent formula uses the tangent of each of the angles in the sum, and the tangent of 90 degrees is undefined, since the cosine of 90 degrees in the denominator is zero. Therefore, the formula would always involve an undefined tangent.

If you are really bored, you could use infinity as the tangent of 90 degrees to solve this.

Tan A+B = (tan A + tan B)/( 1- tanA tanB)
Tan A+B = (tan A/tan B + 1)/(1/tanB - tanA)

If tan B = infinity, this reduces to (0 + 1) / (0 - tanA) = -1/tanA