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Trigonometric Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometric Identities2 Marks
Question
Prove the following identity:
$
(\cos A+\sin A)^2+(\cos A-\sin A)^2=2
$
✓

Answer

$
\begin{aligned}
& \text { LHS }=(\cos A+\sin A)^2+(\cos A-\sin A)^2 \\
& =\cos ^2 A+\sin ^2 A+2 \cos A \cdot \sin A+\cos ^2 A+\sin ^2 A-2 \cos A \cdot \sin A \\
& =2\left(\cos ^2 A+\sin ^2 A\right)=2=\text { RHS }
\end{aligned}
$

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