in proving trigonometric identities if cot theta sin theta = cos theta. what is the correct answer?

prove : cotØsinØ = cosØ

LS = (cosØ/sinØ)(sinØ
= cosØ
= RS

To solve the equation cot(theta)sin(theta) = cos(theta) and determine if it is true or not, we can manipulate the equation using trigonometric identities until we find an identity that matches the given equation.

Let's start by using the reciprocal identity for cotangent: cot(theta) = cos(theta) / sin(theta). We can substitute this expression back into the equation:

(cot(theta))sin(theta) = cos(theta)
(cos(theta) / sin(theta)) * sin(theta) = cos(theta)

Next, we simplify the equation by canceling out sin(theta) on the left-hand side:

(cos(theta) / sin(theta)) * sin(theta) = cos(theta) * sin(theta) / sin(theta)
cos(theta) = cos(theta)

The resulting equation is cos(theta) = cos(theta), which is true for all values of theta.

Therefore, the correct answer is that the equation cot(theta)sin(theta) = cos(theta) is true for all values of theta.