Simplify the expression: cot x sin x - sin + cos x

Solution:

Given expression is

cot x sin x - sinx + cos x

We know by the trigonometric ratio that cotx = cosx/sinx

= cosx/sinx . sinx - sinx + cosx

= cosx - sinx + cosx

= 2cosx - sinx

Therefore,the simplified expression is 2cosx - sinx

Simplify the expression: cot x sin x - sin + cos x

Summary:

cot x sin x - sin + cos x is simplified as 2cosx - sinx.