Question

Can any Math Expert willing to help me out? How do you solve this?

cot(π/6) = 1/tan(π/6)
A) π/3
B) 3/√3
C) √3
D) 1/√3

Answer 1

The answer to cot(π/6) = 1/tan(π/6) is found by knowing that cotangent is the reciprocal of tangent. Therefore, cot(π/6) equals the reciprocal of tan(π/6), which is √3, making the correct answer C) √3.

Step-by-step explanation:

To solve the equation cot(π/6) = 1/tan(π/6), we need to understand the relationship between cotangent and tangent functions. Cotangent is the reciprocal of the tangent function, meaning cot(θ) = 1/tan(θ). Therefore, the equation is true by definition of the cotangent function.

Now, let's evaluate tan(π/6). The tangent of π/6 (which is 30 degrees) can be determined from the unit circle or trigonometric functions of common angles. tan(π/6) = 1/√3, so taking the reciprocal of that, cot(π/6) = √3. Thus, the correct answer is C) √3.