展开 (acos(wt)+bsin(wt))^2

解答

展开

(a cos (wt) + b sin (wt))^{2}

a^{2} cos^{2} (wt) + ab sin (2 wt) + b^{2} sin^{2} (wt)

求解步骤

(a cos (wt) + b sin (wt))^{2}

使用完全平方公式:

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

(a cos (wt) + b sin (wt))^{2} = (a cos (wt))^{2} + 2 a cos (wt) b sin (wt) + (b sin (wt))^{2}

= (a cos (wt))^{2} + 2 a cos (wt) b sin (wt) + (b sin (wt))^{2}

化简

(a cos (wt))^{2} + 2 a cos (wt) b sin (wt) + (b sin (wt))^{2} : a^{2} cos^{2} (wt) + ab sin (2 wt) + b^{2} sin^{2} (wt)

= a^{2} cos^{2} (wt) + ab sin (2 wt) + b^{2} sin^{2} (wt)

e x p an d x ln (x - 4)

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