If α+β=90°, then the maximum value of sin α sin β is

Question

If α+β=90°, then the maximum value of sin α sin β is (A) 1 / 2 (B) 1 / 4 (C) 1 (D) none of these

Tardigrade Admin · Accepted Answer

Let y= sin α sin β Now y= sin α sin (90°-α)= sin α cos α=(1/2)(2 sin α cos α) =(1/2) sin 2 α Now sin 2 α ≤ 1 ⇒ (1/2) sin 2 α ≤ (1/2)

Q. If $α + β = 9 0^{\circ}$ , then the maximum value of $sin α sin β$ is