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 = [tex]\frac{cos \ \theta}{sin \ \theta}[/tex]
L.H.S = sin θ cos θ
so, sin θ cos θ ≠ [tex]\frac{cos \ \theta}{sin \ \theta}[/tex]
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.
