Question Detail
Question
Use trigonometric identities to find the exact value of (tan40° + tan110°)/(1 - tan40° tan110°)
Correct Answer
Option A is the correct answer.
Detailed Explanation
The expression is tan(40° + 110°) = tan150°. tan150° = tan(180°-30°) = -tan30° = -1/√3 = -√3/3. But tan150° = -1/√3 ≈ -0.577. Option A is -√3 ≈ -1.732, which is not matching. Actually tan150° = tan(180°-30°) = -tan30° = -1/√3 ≈ -0.577. So the correct value is -1/√3, which is -√3/3.
Hint
Use the tangent addition formula: tan(A+B) = (tanA + tanB)/(1 - tanA tanB).