Cos(a+b) + cos(пи/2 - a) * cos(пи/2-b) Упростить выражение

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To simplify the expression, we can use the trigonometric identities:

Cos(a+b) = cos(a)cos(b) - sin(a)sin(b)

cos(π/2 - a) = sin(a)

cos(π/2 - b) = sin(b)

Now, substituting these identities into the expression:

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

The expression becomes:

(cos(a)cos(b) - sin(a)sin(b)) + sin(a)sin(b)

Now, we can simplify further:

cos(a)cos(b) - sin(a)sin(b) + sin(a)sin(b)
cos(a)cos(b)

Therefore, the simplified expression is cos(a)cos(b).