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Based on the question, here is the diagram.

The trigonometric function, sin(C) = (opposite side)/ (hypotenuse)

Therefore, sin(C) = AB/AC

This gives: sin(45)= AB/ 4 -> 1/√2= AB/ 4

This implies: AB= 4 * 1/√2 -> 4 * √2/ 2 = 2√2

Therefore the measure of the side, AB= 2√2m

Here let’s start with the left-hand side of the equation -> tan(x)/ cot(x)

We can also write the above expression as: tan(x)/ cot(x) = [sin(x/cos(x)]/ [cos(x)/sin(x)]

Here we can take the reciprocal of the denominator and this gives:

[sin(x)/ cos(x)] * [sin(x)/cos(x)]

This implies: [sin(x)]

[sin(x)/ cos(x)]

Hence proved!