Question

sin^3x-cos^3x если sinx-cosx=0.8

Answer 1

$sin^{3}x-cos^{3}x=(sinx-cosx)(sin^{2}x+sinxcosx+cos^{2}x)= \\ (sinx-cosx)(1+sinxcosx)=0,8(1+0,18)=0,8*1,18=0,944 \\ sinx-cosx=0,8 \\ (sinx-cosx)^{2}=(0,8)^{2} \\ sin^{2}x-2sinxcosx+cos^{2}x=0,64 \\ 1-2sinxcosx=0,64 \\ 2sinxcosx=0,36 \\ sinxcosx=0,18$

Answer 2

Раскладываем sin^3x - cos^3x как 
(sinx-cosx)*(sin^2x + sinxcosx + cos^2x)=(sinx-cosx)(1+sinxcosx)
возведем в квадрат sinx - cosx
sin^2x-2sinxcosx+cos^2x=0.64
-2sinxcosx=-0.36
sinxcosx = 0.18
(sinx-cosx)*(sin^2x + sinxcosx + cos^2x)=(sinx-cosx)(1+sinxcosx)=
=0.8*(1+0.18)=0.944
Вроде должно быть правильно. Быстро писал...

Answer 3

To find the value of the expression sin^3x - cos^3x given that sinx - cosx = 0.8, we can use the identities for the cube of a binomial.

Let's start by rewriting the given expression:

sin^3x - cos^3x

Using the identity for the cube of a binomial, we can rewrite sin^3x and cos^3x as:

(sin x - cos x)(sin^2x + sin x cos x + cos^2x)

Now, let's substitute the value of sinx - cosx = 0.8 into the expression:

(0.8)(sin^2x + sin x cos x + cos^2x)

Next, we can simplify the expression sin^2x + sin x cos x + cos^2x. This expression represents the sum of squares of sine and cosine, which is equal to 1. This is because sin^2x + cos^2x = 1, which is a fundamental identity in trigonometry. Therefore, we can substitute this value into the expression:

(0.8)(1)

Finally, we can simplify the expression:

0.8

So, the value of sin^3x - cos^3x, given that sinx - cosx = 0.8, is 0.8.