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