If-0-lt-a-b-lt-pi-then-prove-that-sin-ab-sin-a-b-2-32a-2-b-2-ab-a-b-5-

Question Number 156448 by MathSh last updated on 11/Oct/21

If 0 < a ⩽ b < π then prove that :

\frac{\sin \sqrt{ab}}{\sin (\frac{a + b}{2})} ⩾ \frac{{32 a}^{2} b^{2} \sqrt{ab}}{{(a + b)}^{5}}

Answered by ghimisi last updated on 11/Oct/21

f (t) = \frac{s i n t}{t^{5}}

\frac{a + b}{2} ⩾ \sqrt{a b} \Rightarrow f (\frac{a + b}{2}) ⩽ f (\sqrt{a b})

Commented by MathSh last updated on 11/Oct/21

Very nice dear Ser, thankyou

Facebook Tweet Pin