Question

How do you verify the identity $\sin \left(90°+A\right)=\cos \left(A\right)$?

Answer 1

Verify the given expression:

It is known that $\sin \left(A+B\right)=\sin \left(A\right)\times \cos \left(B\right)+\cos \left(A\right)\times \sin \left(B\right)$.

Thus,

$\sin \left(90°+A\right)=\sin \left(90°\right)\times \cos \left(A\right)+\cos \left(90°\right)\times \sin \left(A\right)$

$$\begin{gathered} \Rightarrow \sin \left(90°+A\right)=\left(1\right)\times \cos \left(A\right)+\left(0\right)\times \sin \left(A\right) \\ \Rightarrow \sin \left(90°+A\right)=\cos \left(A\right) \end{gathered}$$

Therefore, it is verified that $\sin (90°+\mathrm{A})=\cos \left(A\right)$.