Solve:
${sin}^{2} A - {cos}^{2} A$

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Solution

We have, ${sin}^{2} A - {cos}^{2} A$

Let $x = {sin}^{2} A - {cos}^{2} A$

$= - ({cos}^{2} A - {sin}^{2} A)$

Since,
${cos}^{2} A - {sin}^{2} A = cos 2 A$

Therefore,

$x = - cos 2 A$

Hence, this is the answer.

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Prove it:

Cos²A-cos²A=sin²A-sin²A

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