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Trigonometry – I — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsTrigonometry – I1 Mark
Question
Prove the following : $\cos ^4 \theta-\sin ^4 \theta+1=2 \cos ^2 \theta$
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Answer

$\text { L.H.S. }=\cos ^4 \theta-\sin ^4 \theta+1$
$=\left(\cos ^2 \theta\right)^2-\left(\sin ^2 \theta\right)^2+1=\left(\cos ^2 \theta+\sin ^2 \theta\right) c\left(\cos ^2 \theta-\sin ^2 \theta\right)+1$
$=(1)\left(\cos ^2 \theta-\sin ^2 \theta\right)+1=\cos ^2 \theta+\left(1-\sin ^2 \theta\right)$
$=\cos ^2 \theta+\cos ^2 \theta=2 \cos ^2 \theta=\text { R.H.S. }$

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