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Trigonometric Identities — Mathematics STD 10 — Question

ICSE BoardEnglish MediumSTD 10MathematicsTrigonometric Identities2 Marks
Question
Prove the following identity :
$
\sin ^4 A+\cos ^4 A=1-2 \sin ^2 A \cos ^2 A
$
✓

Answer

$
\begin{aligned}
& \sin ^4 A+\cos ^4 A=1-2 \sin ^2 A \cos ^2 A \\
& \Rightarrow \sin ^4 A+\cos ^4 A+2 \sin ^2 A \cos ^2 A=1 \\
& \text { LHS }=\left(\sin ^2 A+\cos ^2 A\right)^2 \\
& =1=\text { RHS }
\end{aligned}
$

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