Given:
[tex]\cos(\frac{\pi}{2}-x)=\sin x[/tex]
Required:
To find whether the given statement is true or false.
Explanation:
Let,
[tex]\cos(A-B)=\cos A\cos B+\sin A\sin B[/tex]
Therefore,
[tex]\cos(\frac{\pi}{2}-x)=\cos\frac{\pi}{2}\cos x+\sin\frac{\pi}{2}\sin x[/tex]
But
[tex]\begin{gathered} \cos\frac{\pi}{2}=0 \\ \\ \sin\frac{\pi}{2}=1 \end{gathered}[/tex]
So,
[tex]\begin{gathered} \cos(\frac{\pi}{2}-x)=0+(1)\sin x \\ \\ =\sin x \end{gathered}[/tex]
Final Answer:
The given statement is TRUE.
[tex]\cos(\frac{\pi}{2}-x)=\sin x[/tex]
