Question

1-(sina+cos(-a))2/-sin(-a)​

Answer 1

Ответ:

$-2cosa$

Объяснение:

$\frac{1-(sina+cos(-a))^2}{-sin(-a)}=\frac{1-(sin^2a+cos^2a+2sinacosa)}{-(-sina)}=\\\\=\frac{1-(1+2sinacosa)}{sina}=\frac{1-1-2sinacosa}{sina}=\frac{-2sinacosa}{sina}=-2cosa$

Answer 2

Let's simplify the expression step by step:

1. Start with the expression:

   (1 - (sin(a) + cos(-a))^2) / -sin(-a)

2. First, simplify the numerator by expanding the square:

   (1 - (sin(a) + cos(-a))^2) = 1 - (sin(a) + cos(-a))(sin(a) + cos(-a))

3. Use the trigonometric identity: cos(-a) = cos(a) to simplify further:

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

4. Now, expand the square and simplify:

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

5. Notice that sin^2(a) + cos^2(a) is equal to 1 due to the Pythagorean identity, so we can substitute that:

   1 - (1 + 2sin(a)cos(a))

6. Distribute the negative sign:

   1 - 1 - 2sin(a)cos(a)

7. Simplify further:

   -2sin(a)cos(a)

8. Finally, rewrite -sin(-a) as sin(a) (since sine is an odd function):

   (-2sin(a)cos(a)) / sin(a)

9. Cancel out the common factor of sin(a):

   -2cos(a)

So, the simplified expression is:

-2cos(a)