Question

Prove$\sin (90-A)=\cos A$

Answer 1

Prove that:$\sin (90-A)=\cos A$

Use formula:

$\sin (A-B)=\sin A.\cos B-\sin B.\cos A$

Solve the L.H.S part.

$$\begin{gathered} \sin (90°-A)=\sin 90°.\cos A-\sin A.\cos 90°\therefore \mathit{s}\mathit{i}\mathit{n}\mathbf{}\mathbf{90}\mathbf{°}=1and\mathit{c}\mathit{o}\mathit{s}\mathbf{}\mathbf{90}\mathbf{°}=0 \\ \Rightarrow =1.\cos A-\sin A.0 \\ \Rightarrow =\cos A \end{gathered}$$

We can see L.H.S= R.H.S.

Hence, proved.