To find cot x from the equation sin x × cot x × csc x = √2, we can start by breaking down the trigonometric functions involved.
The cotangent function can be defined in terms of sine and cosine:
- cot x = cos x / sin x
The cosecant function is the reciprocal of sine:
- csc x = 1 / sin x
Now, substituting cot x and csc x in the given equation:
- sin x × (cos x / sin x) × (1 / sin x) = √2
The sin x in the numerator and the first sin x in the denominator will cancel out:
- cos x / sin x = √2
This simplifies to:
- cot x = √2
To conclude, we find that:
- cot x = √2
In a real-world context, this means that at certain angles x, the cotangent function will equal the square root of 2, which can be particularly interesting when analyzing various triangles or waves in physics and engineering.