Question

prove that sin theta cos theta = cot theta is not a trigonometric identity by producing a counterexample

Answer 1

Answer:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Begin with the right hand side:

R.H.S = cot θ = $\frac{cos \ \theta}{sin \ \theta}$

L.H.S = sin θ cos θ

so, sin θ cos θ ≠ $\frac{cos \ \theta}{sin \ \theta}$

So, the equation is not a trigonometric identity.

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Anther solution:

To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.

Assume θ with a value and substitute with it.

Let θ = 45°

So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2

R.H.S = cot θ = cot 45 = 1

So, L.H.S ≠ R.H.S

So, sin θ cos θ = cot θ is not a trigonometric identity.