please help me.

use trig. identities to find the exact value.

tan 25° + tan 5° / 1- tan 25° tan 5°

recall

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

I believe you meant to type
(tan 25° + tan 5°) /( 1- tan 25° tan 5°)

now it fits the above pattern and it equals

tan(25+5) = tan 30°

from my 30-60-90 triangle I know that
tan 30° = 1/√3 or √3/3

To find the exact value of the expression using trigonometric identities, we can use the tangent and cotangent addition formulas:

The tangent addition formula states:

tan(x + y) = (tan(x) + tan(y))/(1 - tan(x)tan(y))

Using this formula, we can rewrite the expression as follows:

tan(25° + 5°) / (1 - tan(25°)tan(5°))

Now, we need to determine the values of tan(25°), tan(5°), and tan(25° + 5°) in order to evaluate the expression.

First, let's find the values of tan(25°) and tan(5°) using a scientific calculator or trigonometric tables:

tan(25°) ≈ 0.4663
tan(5°) ≈ 0.0875

Next, we can use the angle addition formula for tangents:

tan(25° + 5°) = (tan(25°) + tan(5°))/(1 - tan(25°)tan(5°))

Substituting the values we found earlier:

tan(25° + 5°) ≈ (0.4663 + 0.0875) / (1 - (0.4663)(0.0875))
≈ 0.5538 / (1 - 0.0408)
≈ 0.5538 / 0.9592
≈ 0.5769

Therefore, the exact value of the expression is approximately 0.5769.