Simplify the expression cot x sin x sin(π/2 – x) cos x

To simplify the expression cot x sin x sin(π/2 - x) cos x, let’s break it down step by step.

First, recall that:

• cot x is the same as cos x / sin x.
• sin(π/2 - x) simplifies to cos x due to the co-function identity.

Now substitute these into the original expression:

cot x sin x sin(π/2 - x) cos x = (cos x / sin x) * sin x * cos x * cos x

The sin x in the numerator and the sin x in the denominator cancel out:

= cos x * cos x = cos2x

So, the simplified expression is:

cos2x

This simplification shows that the original expression reduces neatly to cos2x.