Question #c38f4

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Answer 1 · 2016-10-24T22:35:40

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

Using the identity

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

we can subtract ${sin}^{2} (x)$ $sin^2(x)$ from both sides to obtain

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

With that:

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

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