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Trigonometry – I — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – I1 Mark
Question
Prove the following : $\sin ^4 \theta+\cos ^4 \theta=\sin ^4 \theta+\cos ^4 \theta$
✓

Answer

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

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