Simplify cos(arccot(x))

Problem

cos(arccot(x))

Solution

1. Identify the inner function and set it equal to an angle θ such that θ=arccot(x)

2. Rewrite the expression using the definition of the cotangent function, which gives cot(θ)=x

3. Interpret the cotangent ratio in a right triangle where cot(θ)=adjacent/opposite We can let the adjacent side be x and the opposite side be 1

4. Calculate the hypotenuse using the Pythagorean theorem: a2+b2=c2

c=√(,x2+1)

c=√(,x2+1)

5. Determine the cosine of θ using the ratio cos(θ)=adjacent/hypotenuse

cos(θ)=x/√(,x2+1)

Final Answer

cos(arccot(x))=x/√(,x2+1)

Want more problems? Check here!