Simplify $\sin (90-x)$?

Hint: In this question we have been asked to simplify the given expression $\sin \left( {{90}^{\circ }}-x \right)$ . From the basic concepts of trigonometry we know that the formula given as $\sin \left( A-B \right)=\sin A\cos B-\cos A\sin B$ is valid. Now we will use this formula for answering this question.

Complete step by step answer:
Now considering from the question we have been asked to simplify the given expression $\sin \left( {{90}^{\circ }}-x \right)$ .
From the basic concepts of trigonometry we know that the formula given as $\sin \left( A-B \right)=\sin A\cos B-\cos A\sin B$ is valid.
Now we will use this formula for answering this question.
By using this formula we will have $\sin \left( {{90}^{\circ }}-x \right)=\sin {{90}^{\circ }}\cos x-\cos {{90}^{\circ }}\sin x$ .
From the basic concepts of trigonometry we have been taught the trigonometric table which gives the values of all trigonometric functions for the specified values. We know that the values are given as $\sin {{90}^{\circ }}=1$ and $\cos {{90}^{\circ }}=0$ .
By substituting them in the expression we will have $\sin \left( {{90}^{\circ }}-x \right)=\cos x$ .

Therefore we can conclude that the simplified and reduced form of the given expression $\sin \left( {{90}^{\circ }}-x \right)$ is given as $\cos x$ .

Note: While answering questions of this type we should be sure with our concepts of trigonometry that we are going to apply in the process. This is a very simple and easy question and can be answered in a short span of time. Many of us generally remember these conversions; they do not derive them every time. Very few mistakes are possible in questions of this type. Someone can forget the formula and write it as $\sin \left( A-B \right)=\cos A\cos B-\sin A\sin B$ which will make them end up having the wrong conclusion.