因式分解 cos^{22}(x)-sin^{22}(x)

解答

因式分解

cos^{22} (x) - sin^{22} (x)

(cos^{11} (x) + sin^{11} (x)) (cos^{11} (x) - sin^{11} (x))

求解步骤

cos^{22} (x) - sin^{22} (x)

cos^{22} (x) = (cos^{11} (x))^{2}

sin^{22} (x) = (sin^{11} (x))^{2}

= (cos^{11} (x))^{2} - (sin^{11} (x))^{2}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

(cos^{11} (x))^{2} - (sin^{11} (x))^{2} = (cos^{11} (x) + sin^{11} (x)) (cos^{11} (x) - sin^{11} (x))

= (cos^{11} (x) + sin^{11} (x)) (cos^{11} (x) - sin^{11} (x))

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s im pl i f y l (sin^{2} (2 x))

f a c t or a^{4} b^{3} + a^{3} b^{4}

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