Question

Prove that cos to the power 4 theta-sin to the power 4 theta=cos2theta

Answer 1

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Answer 2

Answer:

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

now, using identity a²-b² = (a-b) (a+b) we get

(cos²x - sin²x)(cos²x + sin²x)

we know that cos²x + sin²x is 1 so we are left with:

cos²x - sin²x

which we know is cos2x