The value of $c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ}$ is

$\frac{\sqrt{5} + 1}{8}$

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$\frac{\sqrt{5} - 1}{8}$

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$\frac{\sqrt{5} + 1}{5}$

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$\frac{\sqrt{5} + 1}{2 \sqrt{2}}$

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Solution

The correct option is A
$\frac{\sqrt{5} + 1}{8}$

Given: $c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ}$

$= c o s (48^{\circ} + 12^{\circ}) - c o s (48^{\circ} - 12^{\circ}) = \frac{1}{2} . \frac{\sqrt{5} + 1}{4} = \frac{\sqrt{5} + 1}{8}$

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Similar questions

{cos}^{2} 48^{\circ} - {sin}^{2} 12^{\circ}

$c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ} =$

c o s^{2} 48^{\circ} - s i n^{2} 12^{\circ}

({cos}^{2} 66^{\circ} - {sin}^{2} 6^{\circ}) ({cos}^{2} 48^{\circ} - {sin}^{2} 12^{\circ})

\cos^{2} 48 ° - \sin^{2} 12 °

\frac{\sqrt{5} + 1}{8}

\frac{\sqrt{5} - 1}{8}

\frac{\sqrt{5} + 1}{5}

\frac{\sqrt{5} + 1}{2 \sqrt{2}}

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