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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