展开 (cos(x)-1)^2

解答

展开

(cos (x) - 1)^{2}

cos^{2} (x) - 2 cos (x) + 1

求解步骤

(cos (x) - 1)^{2}

使用完全平方公式:

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

(cos (x) - 1)^{2} = cos^{2} (x) - 2 cos (x) \cdot 1 + 1^{2}

= cos^{2} (x) - 2 cos (x) \cdot 1 + 1^{2}

化简

cos^{2} (x) - 2 cos (x) \cdot 1 + 1^{2} : cos^{2} (x) - 2 cos (x) + 1

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

s im pl i f y (x - y) (x + y)

e x p an d (9 + 2 x sin (y)) d x - x^{2} cos (y) d y

e x p an d \frac{4 x ^{3} - x ^{2} - 3 x - 2}{x ^{2} ( x + 1 ) ^{2}}

e x p an d (sec (a) + tan (a)) (1 - sin (a))

e x p an d \frac{( p - q ) ^{3}}{p + q}