Prove that sin x cos x = cot x is not a trigonometric identity by producing a counterexample.

see below

Step-by-step explanation:

sin x cos x = cot x

We need to show a counter example

Let's use 30 degrees

sin 30 cos 30 = cot 30

1/2 * sqrt (3) / 2 = sqrt (3)

sqrt (3) / 4 = sqrt (3)

not true

Step-by-step explanation:

sin (60) = sqrt (3) / 2

cos (60) = ½

tan (60) = sqrt (3)

cot (60) = 1/sqrt (3) = sqrt (3) / 3

sin (60) cos (60) = cot (60)

sqrt (3) / 2 * ½ = sqrt (3) / 3

sqrt (3) / 4 = sqrt (3) / 3

Is a FALSE statement.

So the equation is not true for x = 60. Hence, not an identity