Question

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

cos x

sin x

2 sin x

2 cos x

Answer 1

Option A

Explanation:

Given expression:
`cotx* sinx-sin((\pi )/(2)-x)+cosx`

Simplifying the expression :

`cotx* sinx-sin((\pi)/(2)-x)+cosx`

applying property of trigonometry,

`cotx=(cosx)/(sinx)` and
`sin((\pi)/(2)-x)=cosx`

we get,

`=(cosx)/(sinx)* sinx-cosx+cosx`

`=cosx-cosx+cosx`

`=cosx`

Therefore, option A is correct

Answer 2

The best and most correct answer among the choices your question about trigonometric expressions provided is the first choice which is cos x.

cotx sinx - sin(π/2-x) + cosx
= cosx/sinx * sinx - cosx + cosx
= cosx - cosx + cosx
= cosx

I hope it has come to your help.