已知sinα-cosα=根号2/2,求sin3次方α+cos3次方α的值
网友回答
sinα-cosα=根号2/2
平方得到：1-2sinacosa=1/2
sinacosa = 1/4
sina+cosa = ±√6/2
sin3次方α+cos3次方α
=(sina+cosa)(1-sinacosa)
=±√6/2(1-1/4)
=±3√6/8
======以下答案可供参考======
供参考答案1:
两个值0.9186
-0.9186
供参考答案2:
clc; clear; close all
f = sym('sin(x)-cos(x)-sqrt(2)/2');
X = solve(f, 'x');
F = sym('sin(x)^3+cos(x)^3');
out = subs(F, 'x', double(X));