Find the Exact Value tan(24)

Problem

tan(24^∘)

Solution

1. Identify the goal as finding the exact value of tan(24^∘)

2. Use the angle subtraction formula for tangent, tan(A−B)=(tan(A)−tan(B))/(1+tan(A)*tan(B)) with A=60^∘ and B=36^∘

3. Determine the value of tan(60^∘)=√(,3)

4. Determine the value of tan(36^∘)=√(,5−2√(,5))

5. Substitute these values into the subtraction formula.

6. Simplify the resulting expression to represent the exact value.

Final Answer

tan(24^∘)=(√(,3)−√(,5−2√(,5)))/(1+√(,3)√(,5−2√(,5)))

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