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

COS (1-x) X sin x O A. True B. False-example-1
User Steffi
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1 Answer

22 votes
22 votes

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

User Shazz
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