Question

If A + B =90°
sin A cosB + Cos A sin B​

Answer 1

A + B = 90

A = B - 90 ----------- I

In, sin(A)cos(B) + cos(A)sin(B) we substitute I

sin(-(90 - B))cos(B) + cos(-(90 - B))sin(B)

- cos(B)cos(B) + sin(B)sin(B)

$sin^{2}$(B) - $cos^{2}$(B)

- cos(2B)

Hence, the value of sin(A)cos(B) + cos(A)sin(B)

when, A + B = 90 is - cos(2B)