Sum and diffence formula Finding Exact value of Tan 105-Tan 10)-15)/1+ tan(105)Tan(-15)
86.16 i believe
Hard to say, due to the typos, but it looks like you want
tan(105-(-15)) = tan(120) = -tan(60) = -√3
To find the exact value of the expression:
Tan(105°) - Tan(10°) - 15 / (1 + Tan(105°) * Tan(-15°))
We can use the sum and difference formulas for tangent to simplify the expression. The sum and difference formulas for tangent are:
Tan(A ± B) = (Tan(A) ± Tan(B)) / (1 ∓ Tan(A) * Tan(B))
Let's break down the expression step by step:
1. Start with the expression:
Tan(105°) - Tan(10°) - 15 / (1 + Tan(105°) * Tan(-15°))
2. Apply the sum and difference formula for tangent to the first two terms:
(Tan(105° + (-10°))) / (1 + Tan(105°) * Tan(-10°)) - 15 / (1 + Tan(105°) * Tan(-15°))
Note: We changed the subtraction between two tangent values to an addition using the formula.
3. Simplify the expression further:
(Tan(95°)) / (1 + Tan(105°) * Tan(-10°)) - 15 / (1 + Tan(105°) * Tan(-15°))
4. Apply the sum and difference formula for tangent to the second term:
(Tan(95°)) / (1 + (Tan(105° + (-15°)))) - 15 / (1 + Tan(105°) * Tan(-15°))
Note: We changed the addition between two tangent values to a subtraction using the formula.
5. Simplify the expression further:
(Tan(95°)) / (1 + Tan(90°)) - 15 / (1 + Tan(105°) * Tan(-15°))
6. Since Tan(90°) is undefined, we cannot evaluate the expression any further.
Therefore, the exact value of the expression is undefined.