How do you simplify ${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} (x) + {cos}^{2} (x)$ $sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)$ ?

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How do you simplify ${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} (x) + {cos}^{2} (x)$ $sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)$ ?

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Answer 1 · 2016-10-21T06:21:55

${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} x + {cos}^{2} (x) = 0$ $sin^4(x) - cos^4(x)-sin^(2)x+cos^2(x) = 0$

Explanation:

Use:

$a^{2} - b^{2} = (a - b) (a + b)$ $a^2-b^2 = (a-b)(a+b)$

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

as follows:

${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} (x) + {cos}^{2} (x)$ $sin^4(x) - cos^4(x)-sin^(2)(x)+cos^2(x)$

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

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

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

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

$= 0$ $= 0$

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How do you simplify ${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} (x) + {cos}^{2} (x)$ $sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)$ ?

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Explanation:

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How do you simplify sin4(x)−cos4(x)−sin2(x)+cos2(x)sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x) ?

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How do you simplify ${sin}^{4} (x) - {cos}^{4} (x) - {sin}^{2} (x) + {cos}^{2} (x)$ $sin^4(x)-cos^4(x)-sin^2(x)+cos^2(x)$ ?