因式分解 cos^5(x)+sin^5(x)

解答

因式分解

cos^{5} (x) + sin^{5} (x)

(cos (x) + sin (x)) (cos^{4} (x) - cos^{3} (x) sin (x) + sin^{2} (x) cos^{2} (x) - sin^{3} (x) cos (x) + sin^{4} (x))

求解步骤

cos^{5} (x) + sin^{5} (x)

使用因式分解法则

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1})

n is odd

cos^{5} (x) + sin^{5} (x) = (cos (x) + sin (x)) (cos^{4} (x) - sin (x) cos^{3} (x) + sin^{2} (x) cos^{2} (x) - sin^{3} (x) cos (x) + sin^{4} (x))

= (cos (x) + sin (x)) (cos^{4} (x) - sin (x) cos^{3} (x) + sin^{2} (x) cos^{2} (x) - sin^{3} (x) cos (x) + sin^{4} (x))

f a c t or 3 (2 x + 1) (x + 5) (2 x + 1)

f a c t or 3^{2} + 5 x + 2

f a c t or 2 lo g_{2 l e f t (x^{4 r i g h t})} (x)

f a c t or 2 x^{- 2} - 3 x^{- 3}

f a c t or (d + 1) - 5 (d + 1)