Find the Exact Value tan(25 degrees )

Problem

tan(25^∘)

Solution

1. Identify the expression as the tangent of 25^∘ Since 25^∘ is not a standard angle on the unit circle, we express it in terms of half-angle or sum/difference identities.

2. Apply the half-angle formula for tangent, which is tan(θ/2)=(1−cos(θ))/sin(θ)

3. Substitute θ=50^∘ into the formula to get tan(25^∘)=(1−cos(50^∘))/sin(50^∘)

4. Recognize that while this provides a trigonometric representation, the exact algebraic value involving radicals is typically derived from the roots of a polynomial or expressed using the values of 5^∘ or 10^∘

5. State the value in its simplest trigonometric form or its decimal approximation if an algebraic radical form is not requested, as the radical form for 25^∘ is extremely complex.

Final Answer

tan(25^∘)=(1−cos(50^∘))/sin(50^∘)

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