Question

Demostrati ca in orice triunghi dreptunghic ABC cu masura lu' A=90 de grade are loc inegalitatea : sin B · cos B ≤ sin 30 grade. Va rog frumos.... :)

Answer 1

conform formulei 
$sin(a)cos(b) = \frac{sin(a+b)+sin(a-b)}{2}$
rezulta ca
sin(b)cos(b) = $\frac{sin(2b)+sin(0)}{2} = \frac{sin(2b)}{2}$
orice sin este ≤ 1 ⇒ sin(b)cos(b) =  $\frac{sin(2b)}{2}$ ≤ $\frac{1}{2}$
or, cum sin(30) =  $\frac{1}{2}$ ⇒ sin(b) x cos(b) ≤ sin(30)