Question

If in a ∆ABC, ∠C = 90°, then the maximum value of sin A sin B is 

(A)  1/2

(B)  1 

(C)  2 

(D)  None of these

Answer 1

Correct option (A)  1/2

sinA sinB = 1/2 x 2 sinAsinB

= 1/2[cos(A - B)-cos(A + B)] = 1/2[cos(A-B) - cos 90°]

= 1/2cos(A - B)≤ 1/2

⇒ Maximum value of sinA sinB = 1/2