Question

if cos(alpha + beta)=0 then what will be the value of sin(alpha - beta)

Answer 1

since cos(a+b) = 0, a+b = pi/2
so, b = pi/2 - a and

sin(a-b) = sin(a-pi/2+a)
= sin(2a-pi/2)
= -sin(pi/2 - 2a)
= -cos(2a)
or, since a = pi/2 - b
= -cos(2(pi/2-b))
= -cos(pi-2b)
= cos(2b)