Simplify the expression: cot x sin x - sin quantity pi divided by two minus x. + cos x

Solution:

cot x sin x - sin quantity pi divided by two minus x. + cos x

It can be mathematically written as

cot x sin x - sin (π/2 - x) + cos x

We know that

cot x = cos x / sin x

sin (π/2 - x) = cos x

So we get

= cosx / sinx sinx - cos x + cos x

By further simplification

= cos x - cos x + cos x

= cos x

Therefore, cot x sin x - sin quantity pi divided by two minus x. + cos x by simplification is cos x.

Simplify the expression: cot x sin x - sin quantity pi divided by two minus x. + cos x

Summary:

By simplifying the expression cot x sin x - sin quantity pi divided by two minus x. + cos x we get cos x.