The correct option is C cos 2θ cos ^ 2 ( π #160; 2 +θ #160; ) #160; sin ^ 2 ( π #160; 2 θ #160; ) #160; =( sinθ #160; ...

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Trigonometric Identities

cos2 π/2+θ -s...

Question

$c o s^{2} (\frac{π}{2} + θ) - s i n^{2} (\frac{π}{2} - θ) =$

\frac{1}{2} c o s 2 θ

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- c o s 2 θ

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none of the above

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Solution

The correct option is C $- c o s 2 θ$
${cos}^{2} (\frac{π}{2} + θ) - {sin}^{2} (\frac{π}{2} - θ)$
$= {(- sin θ)}^{2} - {(cos θ)}^{2}$
$= {sin}^{2} θ - {cos}^{2} θ$
$= - ({cos}^{2} θ - {sin}^{2} θ)$
$= - cos 2 θ$
Hence, the answer is $- cos 2 θ .$

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