Question

Упростить (sin(a)-cos(a))^2+(cos(a)+sin(a))^2-2

Answer 1

Надеюсь понятно

Удачи

Answer 2

To simplify the expression $(\sin(a)-\cos(a))^2+(\cos(a)+\sin(a))^2-2$, we'll first expand the squares and then combine like terms:

$(\sin(a)-\cos(a))^2 = \sin^2(a) - 2\sin(a)\cos(a) + \cos^2(a)$

$(\cos(a)+\sin(a))^2 = \cos^2(a) + 2\sin(a)\cos(a) + \sin^2(a)$

Now, let's add these two expressions and simplify:

$(\sin^2(a) - 2\sin(a)\cos(a) + \cos^2(a)) + (\cos^2(a) + 2\sin(a)\cos(a) + \sin^2(a)) - 2$

Simplify the expression:

$= \sin^2(a) + \cos^2(a) + \sin^2(a) + \cos^2(a) - 2$

Since $\sin^2(a) + \cos^2(a) = 1$ (due to the Pythagorean identity), the expression simplifies to:

$= 1 + 1 - 2 = 2 - 2 = 0$

So, the simplified form of the expression is $0$.