Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.

(tan(π/2)+tan((2π)/3))
/
(1-tan(π/2)tan((2π)/3))

Answer=__________
Exact value answer=_________

~Thank you.. I thought it was undefined, apparently not.

Your expression exactly matches the expansion for

tan(A+B)

so you would get tan(π/2 + 2π/3)
= tan 7π/6
= .....

Ahh Surprised I didn't see that.. Thank you.. The exact value would be .5773 right?

To simplify the expression, we can use the tangent addition formula:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In this case, A = π/2 and B = 2π/3. So, the expression becomes:

tan(π/2 + 2π/3) / (1 - tan(π/2)tan(2π/3))

Using the formula, we have:

tan(π/2 + 2π/3) = (tan(π/2) + tan(2π/3)) / (1 - tan(π/2)tan(2π/3))

Now, let's plug in the values:

tan(π/2) = undefined (as the tangent of π/2 is undefined)
tan(2π/3) = sqrt(3)

Now substitute these values into the expression:

(undefined + sqrt(3)) / (1 - undefined * sqrt(3))

Since the numerator is undefined, the value of the expression is also undefined.

Hence, the answer is undefined, and there is no exact value for this expression.

To rewrite the expression, we can use the addition formula for tangent:

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B))

In the given expression, A = π/2 and B = 2π/3. So, we have:

(tan(π/2) + tan((2π)/3)) / (1 - tan(π/2)tan((2π)/3))

Using the addition formula, we can rewrite the numerator and denominator as a single tangent function:

= tan(π/2 + (2π)/3) / (1 - tan(π/2)tan((2π)/3))

Simplifying further, we get:

= tan((3π/6) + (4π/6)) / (1 - tan(π/2)tan((2π)/3))

= tan(π) / (1 - tan(π/2)tan((2π)/3))

Now, we can evaluate this expression.

The tangent of π is undefined, as it is the point where the graph of tangent has vertical asymptotes or goes to infinity. So, the expression is indeed undefined.