Simplify cot(45)

Problem

cot(45^∘)

Solution

1. Identify the trigonometric identity for the cotangent function, which is the ratio of the cosine function to the sine function.

cot(θ)=cos(θ)/sin(θ)

2. Substitute the given angle of 45^∘ into the identity.

cot(45^∘)=cos(45^∘)/sin(45^∘)

3. Evaluate the sine and cosine of 45^∘ using the unit circle or special right triangles, where sin(45^∘)=√(,2)/2 and cos(45^∘)=√(,2)/2

cot(45^∘)=√(,2)/2/√(,2)/2

4. Simplify the fraction by dividing the identical numerator and denominator.

cot(45^∘)=1

Final Answer

cot(45^∘)=1

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