+315 if \(tan~x = \frac{2ab}{a^2 - b^2},\)
where a>b>0 and \(0^\circ < x < 90^\circ,\) then find sin x in terms of a and b
+23252 Picture a right triangle with angle(x) being an acute angle;
then, the side opposite to angle(x) = 2ab
and the side adjacent to angle(x) = a2 - b2.
Finding the hypotenuse: hyp2 = (a2 - b2)2 + (2ab)2
= [ a4 -2a2b2 + b4 ] + [ 4a2b2 ]
= a4 + 2a2b2 + b4
= (a2 + b2)2
---> hypotenuse = a2 + b2
sin(x) = opposite / hypotenuse = 2ab / (a2 + b2)
