Simplify cos(65)

Problem

cos(65)

Solution

1. Identify the expression as the cosine of an angle measured in degrees.

2. Determine if the angle is a standard reference angle (such as 0 30 45 60 or 90.

3. Recognize that 65 is not a standard angle, so its exact value cannot be expressed using simple radicals like √(,3)/2 or 1/2

4. Conclude that the expression is already in its simplest exact form, or it can be expressed in terms of its cofunction using the identity cos(θ)=sin(90−θ)

5. Apply the cofunction identity: cos(65)=sin(90−65)=sin(25)

Final Answer

cos(65)=sin(25)

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