Question

Sin(π\2-a)×cos(π+a) / cos(3π/2+a)​

Answer 1

Формулы приведения:
sin(pi/2-a)=cos(a)
Cos(pi+a)=-cos(a)
Cos(3pi/2+a)=sin(a)
Имеем:
cos(a)•(-cos(a))/sin(a)=-ctg(a)•cos(a)

Answer 2

To simplify the expression sin(π/2 - a) * cos(π + a) / cos(3π/2 + a), we can use trigonometric identities to simplify each term:

1. sin(π/2 - a) = cos(a)
2. cos(π + a) = -cos(a)
3. cos(3π/2 + a) = -sin(a)

Now, substitute these values back into the expression:

(cos(a) * (-cos(a))) / (-sin(a))

Now, we can simplify further:

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

Finally, simplify by canceling the negative signs:

cos(a)^2 / sin(a)

So, sin(π/2 - a) * cos(π + a) / cos(3π/2 + a) simplifies to cos(a)^2 / sin(a).