Question

COS (1-x) X sin x O A. True B. False

Answer 1

Given:

`\cos((\pi)/(2)-x)=\sin x`

Required:

To find whether the given statement is true or false.

Step-by-step explanation:

Let,

`\cos(A-B)=\cos A\cos B+\sin A\sin B`

Therefore,

`\cos((\pi)/(2)-x)=\cos(\pi)/(2)\cos x+\sin(\pi)/(2)\sin x`

But

`\begin{gathered} \cos(\pi)/(2)=0 \\ \\ \sin(\pi)/(2)=1 \end{gathered}`

So,

`\begin{gathered} \cos((\pi)/(2)-x)=0+(1)\sin x \\ \\ =\sin x \end{gathered}`

Final Answer:

The given statement is TRUE.

`\cos((\pi)/(2)-x)=\sin x`