To find cot x given the equation sin x cot x csc x = √2, we can start by using the definitions of the trigonometric functions involved.
First, we know that:
- csc x is defined as 1/sin x
- cot x is defined as cos x/sin x
Substituting these definitions into the equation:
sin x (cos x/sin x) (1/sin x) = √2
This simplifies to:
cos x / sin x = √2
Thus, we have:
cot x = √2
Now, we have found that:
- cot x = √2
This means that in a right triangle where the angle x is involved, the adjacent side is √2 times the opposite side. Therefore, we can conclude that the ratio of the adjacent side to the opposite side for this angle x is √2, which satisfies the equation provided.