Question

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

Answer 1

Answer:

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

Answer 2

Answer:

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