Question:
Write the value of $\sin A \cos \left(90^{\circ}-A\right)+\cos A \sin \left(90^{\circ}-A\right)$.
Solution:
We have,
$\sin A \cos \left(90^{\circ}-A\right)+\cos A \sin \left(90^{\circ}-A\right)=\sin A \sin A+\cos A \cos A$
$=\sin ^{2} A+\cos ^{2} A$
We know that, $\sin ^{2} A+\cos ^{2} A=1$
Therefore, $\sin A \cos \left(90^{\circ}-A\right)+\cos A \sin \left(90^{\circ}-A\right)=1$