I do not understand how to do this problem
((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A
note that all the trig terms are closed right after there A's
example
sin A cos A
=
sin (A) cos (A)
I wrote it out like this
0 = - sin^6 A - cos^6 A + 2sin^3 A cos^3 A - 2sin^3 A - 3sin^2 A cos^2 A - 2sinA cosA + 1
I graphed the problem and my solution and got the same line so my questio is how do i simplify thank you????
use graphic techiques in radians I found that it is roughly equal to
-.5 sin [ 20.42036^-1(x + 40.84071)pi ] + 1
that didn't get me any were lol
To simplify the given expression ((sin^3 A + cos^3 A)/(sin A + cos A)), we can start by factoring the numerator and denominator.
Step 1: Factor the numerator.
Using the identity a^3 + b^3 = (a + b)(a^2 - ab + b^2), we can rewrite sin^3 A + cos^3 A as (sin A + cos A)(sin^2 A - sin A cos A + cos^2 A).
Step 2: Factor the denominator.
Again, using the identity a + b = (a + b)(a^2 - ab + b^2), we can rewrite sin A + cos A as (sin A + cos A)(sin^2 A - sin A cos A + cos^2 A).
Thus, the simplified form of the expression is:
((sin A + cos A)(sin^2 A - sin A cos A + cos^2 A))/((sin A + cos A)(sin^2 A - sin A cos A + cos^2 A))
Step 3: Cancel out the common factors.
Since (sin A + cos A) appears in both the numerator and denominator, we can cancel it out, leaving us with:
(sin^2 A - sin A cos A + cos^2 A)/(sin^2 A - sin A cos A + cos^2 A)
Step 4: Simplify further.
Observe that the terms in the numerator and denominator contain the same terms but written in different order, so they can be rearranged.
(sin^2 A + cos^2 A - sin A cos A)/(sin^2 A - sin A cos A + cos^2 A)
Using the identity sin^2 A + cos^2 A = 1, we can simplify the above expression as follows:
(1 - sin A cos A)/(sin^2 A - sin A cos A + cos^2 A)
Finally, using the identity sin^2 A + cos^2 A = 1 again, we can simplify further:
1 - sin A cos A)/(1 - sin A cos A)
The simplified expression is 1.
Therefore, the given expression ((sin^3 A + cos^3 A)/(sin A + cos A)) is equal to 1 - sin A cos A.