The points `A(0, 0), B(cos alpha, sin alpha) and C(cos beta, sin beta)` are the vertices of a right angled triangle if :

Options

A. `(1)/(2)`
B. `(1)/(sqrt(2))`
C. `(1)/(sqrt(3))`
D. none of these

Answer

B

Explanation

We have, OA=OB=1
and `AB=sqrt(2-2cos(alpha-beta))=|sin((alpha-beta)/(2))|`
Since `DeltaAOB` is a right triangle. Thereofore,
`AB=sqrt(OA^(2)+OB^(2))`
`rArr2|sin(alpha-beta)/(2)|=sqrt(2)rArr|sin(alpha-beta)/(2)|=(1)/(sqrt(2))`