Reciprocal identity equal to cot(x)
1/tan(x)
The reciprocal identity for cot(x) is equal to tan(x). This means that if cot(x) is a given trigonometric function that represents the reciprocal of the tangent function, then the reciprocal identity for cot(x) is simply tan(x).
To understand this, we need to recall the definitions of cotangent (cot) and tangent (tan) functions.
The cotangent function (cot(x)) is defined as the ratio of the adjacent side to the opposite side in a right triangle. Mathematically, cot(x) can be expressed as:
cot(x) = adjacent side / opposite side
On the other hand, the tangent function (tan(x)) is defined as the ratio of the opposite side to the adjacent side in a right triangle. Mathematically, tan(x) can be expressed as:
tan(x) = opposite side / adjacent side
To find the reciprocal identity for cot(x), we need to take the reciprocal of cot(x), which means inverting the fraction:
1 / cot(x) = 1 / (adjacent side / opposite side)
Using the rule of reciprocals, we can rewrite this as:
1 / cot(x) = opposite side / adjacent side
Which is the exact same definition as tan(x). Therefore, the reciprocal identity for cot(x) is equal to tan(x).
In summary, the reciprocal identity for cot(x) is tan(x). This means that the reciprocal of the cotangent function is the tangent function.
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