展开 (cos(5x)+cos(10x)+cos(15x))^2

解答

展开

(cos (5 x) + cos (10 x) + cos (15 x))^{2}

cos^{2} (5 x) + cos (5 x) cos (10 x) + cos (5 x) cos (15 x) + cos (10 x) cos (5 x) + cos^{2} (10 x) + cos (10 x) cos (15 x) + cos (15 x) cos (5 x) + cos (15 x) cos (10 x) + cos^{2} (15 x)

求解步骤

(cos (5 x) + cos (10 x) + cos (15 x))^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(cos (5 x) + cos (10 x) + cos (15 x))^{2} = (cos (5 x) + cos (10 x) + cos (15 x)) (cos (5 x) + cos (10 x) + cos (15 x))

= (cos (5 x) + cos (10 x) + cos (15 x)) (cos (5 x) + cos (10 x) + cos (15 x))

打开括号

= cos (5 x) cos (5 x) + cos (5 x) cos (10 x) + cos (5 x) cos (15 x) + cos (10 x) cos (5 x) + cos (10 x) cos (10 x) + cos (10 x) cos (15 x) + cos (15 x) cos (5 x) + cos (15 x) cos (10 x) + cos (15 x) cos (15 x)

化简

cos (5 x) cos (5 x) + cos (5 x) cos (10 x) + cos (5 x) cos (15 x) + cos (10 x) cos (5 x) + cos (10 x) cos (10 x) + cos (10 x) cos (15 x) + cos (15 x) cos (5 x) + cos (15 x) cos (10 x) + cos (15 x) cos (15 x) : cos^{2} (5 x) + cos (5 x) cos (10 x) + cos (5 x) cos (15 x) + cos (10 x) cos (5 x) + cos^{2} (10 x) + cos (10 x) cos (15 x) + cos (15 x) cos (5 x) + cos (15 x) cos (10 x) + cos^{2} (15 x)

= cos^{2} (5 x) + cos (5 x) cos (10 x) + cos (5 x) cos (15 x) + cos (10 x) cos (5 x) + cos^{2} (10 x) + cos (10 x) cos (15 x) + cos (15 x) cos (5 x) + cos (15 x) cos (10 x) + cos^{2} (15 x)

e x p an d \frac{3 h}{[ ( x + 7 ) ( x + h + 7 ) ]}

s im pl i f y 2 (62329 - 223)

s im pl i f y 2 (7^{\frac{1}{12}} - 1)

e x p an d (5 x^{2} + 5)^{\circ} (2 x + 1)

s im pl i f y (A e^{im θ} + B e^{- im θ})^{2}