Show that the following statement is an identity by transforming the left side into the right side.

sinθ(cscθ − sinθ)= cos^2 θ

csc = 1 / sin

distributing ... 1 - sin^2 = cos^2

To show that the left side of the equation is equal to the right side, we need to simplify both sides and show that they are indeed equal.

Starting with the left side of the equation:
sinθ(cscθ − sinθ)

First, let's convert cscθ to its reciprocal form:
cscθ = 1/sinθ

Substituting this back into the equation, we have:
sinθ(1/sinθ - sinθ)

Next, let's find a common denominator for the terms inside the parentheses:
sinθ(1/sinθ - sin^2θ/sinθ)

Combining the terms inside the parentheses, we obtain:
sinθ - sin^2θ

Now, let's simplify the right side of the equation:
cos^2θ

Since cos^2θ is the square of the cosine function, we can use the Pythagorean identity to relate it to sine:
cos^2θ = 1 - sin^2θ

Thus, we have shown that both sides of the equation are equal, as the left side simplifies to sinθ - sin^2θ, and the right side is equal to 1 - sin^2θ. Therefore, the given statement is an identity.