Question

Cos(а-П/2)-sin(a-П/2)​

Answer 1

cos(a - $\pi$/2) - sin (a - $\pi$/2) = cos(-($\pi$/2 - a) - sin(-($\pi$/2 - a) = cos($\pi$/2 - a) + sin($\pi$/2 -a) = sin(a) + cos(a)

Answer 2

The expression you provided, "cos(а-П/2)-sin(a-П/2)," can be simplified using trigonometric identities.

1. Start by using the trigonometric identity for the difference of two angles:

   cos(A - B) = cos(A)cos(B) + sin(A)sin(B)

2. In your expression, A = a and B = π/2. So, you have:

   cos(a - π/2) = cos(a)cos(π/2) + sin(a)sin(π/2)

3. The values of cos(π/2) and sin(π/2) are:

   cos(π/2) = 0 sin(π/2) = 1

4. Substitute these values into the expression:

   cos(a) * 0 + sin(a) * 1

5. Anything multiplied by 0 is 0, so the expression simplifies to:

   0 + sin(a)

So, the simplified expression is simply sin(a).