Question

Write an algebraic expression equivalent to cot(arctan(x)).

a) x
b) 1/x
c) √(1 + x²)
d) 1/√(1 + x²)

Answer 1

To find an expression equivalent to cot(arctan(x)), we consider the definition of arctan(x) using a right triangle. The cotangent is the reciprocal of the tangent, therefore cot(arctan(x)) simplifies to 1/x.

Step-by-step explanation:

To find an expression equivalent to cot(arctan(x)), we consider the definition of arctan(x) using a right triangle. The cotangent is the reciprocal of the tangent, therefore cot(arctan(x)) simplifies to 1/x. The student has asked to write an algebraic expression equivalent to cot(arctan(x)).

Step-by-step explanation:

Recognize that arctan(x) is the angle whose tangent is x.

Since tan(θ) = opposite/adjacent, in a right triangle where θ is the angle, if tan(θ) = x, that implies opposite/adjacent = x/1.

To find cot(θ), which is the reciprocal of tan(θ), we need the adjacent/opposite. From the triangle, we can say adjacent = 1 and opposite = x, therefore cot(θ) = 1/x.

Therefore, the expression equivalent to cot(arctan(x)) is 1/x.