Answer:
cmon man
Explanation:
We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.
Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.
Multiplying both sides by sinθ, we get:
sin^2θ cosθ = cosθ
Dividing both sides by cosθ, we get:
sin^2θ = 1
Taking the square root of both sides, we get:
sinθ = ±1
So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.
Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:
sin(π/2 + kπ) = ±1
cos(π/2 + kπ) = 0
cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)
Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.