Question

Sin^4 x-cos^4 x=1-2cos^2 x

Answer 1

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$\huge\bold\red{{solution:-}}$

${LHS}:-$

${sin}^{4}x-{cos}^{4}x=$$({sin}^{2}x-{cos}^{2}x)({sin}^{2}+{cos}^{2}x)$

➪Factor

$=({sin}^{2}x-{cos}^{2}x).1$

$=(1-{cos}^{2}x-{cos}^{2}x)$

➪Use the property,

${sin}^{2}x +{cos}^{2}x=1$

$1-2{cos}^{2}x$

$={RHS}$

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