Write the value of (90^ -A)+ (90^ -A). - Vidyadip

Question

Write the value of $\sin\text{A}\cos(90^\circ-\text{A})+\cos\text{A}\sin(90^\circ-\text{A})$.

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Answer

$\sin\text{A}\cos(90^\circ-\text{A})+\cos\text{A}\sin(90^\circ-\text{A})$
$=\sin\text{A}\sin\text{A}+\cos\text{A}\cos\text{A}$
$\begin{cases}\because \cos(90^\circ-\text{A})=\sin\text{A} \\ \sin(90^\circ-\text{A})=\cos\text{A} \\ \sin^2\text{A}+\cos^2\text{A}=1\end{cases}$
$=\sin^2\text{A}+\cos^2\text{A}=1$

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