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Question Bank - P2 — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsQuestion Bank - P23 Marks
Question
$\sin ^4 A-\cos ^4 A=1-2 \cos ^2 A$. For proof of this complete the activity given below.
Activity:
$ \text { L.H.S }=\square$
$=\left(\sin ^2 A +\cos ^2 A \right)(\square)$
$=1(\square) \quad \ldots . .\left[\sin ^2 A +\square=1\right]$
$=\square-\cos ^2 A . \ldots . .\left[\sin ^2 A =1-\cos ^2 A \right]$
$=\square$
$=\text { R.H.S } $
✓

Answer

$\text { L.H.S }=\sin ^4 A -\cos ^4 A =\left(\sin ^2 A\right)^2-\left(\cos ^2 A\right)^2$
$=\left(\sin ^2 A+\cos ^2 A\right)\left(\sin ^2 A -\cos ^2 A \right) \ldots . .\left[\because a^2-b^2=(a+b)(a-b)\right]$
$=1\left(\sin ^2 A -\cos ^2 A \right) \ldots . .\left[\because \sin ^2 A+\cos ^2 A =1\right]$
$=\sin ^2 A-\cos ^2 A$
$=1-\cos ^2 A -\cos ^2 A \ldots \ldots\left[\sin ^2 A=1-\cos ^2 A\right]$
$=1-2 \cos ^2 A$
$=\text { R.H.S }$

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