Let a = sin(t) + tan(t) and b = tan(t) - sin(t). Find (a^2 - b^2)^2/(ab).
+128406 a^2 = sin^2(t) + 2sin(t )tan(t) + tan^2 (t)
b^2 = sin^2( t) - 2sin (t)tan (t) + tan^2( t)
a^2 - b^2 = 4sin(t)tan(t) ⇒ (a^2 - b^2)^2 = 4sin^2(t) tan^2(t)
ab = tan^2(t) - sin^2 (t)
(a^2 - b^2)^2
_____________ =
ab
4sin^2 (t) tan^2 (t)
________________ =
tan^2(t) - sin^2(t)
4 sin^2(t) sin^2(t) / cos^2(t)
_______________________________ =
[sin^2(t) - sin^2(t) cos^2(t)] / cos^2(t)
4 sin^2(t) (sin^2(t)
____________________ =
sin^2 (t) ( 1 - cos^2(t) )
4 sIn^2(t) sin^2(t)
________________ =
sin^2(t) sin^2(t)
4
