The Boolean Gemini Scout Rifle is probably one of the easiest Year 2 Exotics to find in Destiny: The Taken King. There are no excruciatingly challenging Crucible requirements or ultra high-level missions to complete - you just have to finish a few quest chains. Here's how to get it.
After you've completed the first Taken King quest, head over to the Reef and talk to Petra Venj to get the quest called The Taken War: Petra. Accept the quest and head over to Variks (the Fallen NPC in the Reef) and grab the quest called The Wolves of Mars. Complete both of those quest-lines then return to Petra.
When you've finished both The Taken War: Petra and the The Wolves of Mars quest lines (netting yourself a sweet Legendary class item and armor shader from Variks), talk to Petra and you will receive an Exotic quest called The Lost and Found. Note: if the quest does not appear immediately, wait until the next day and check again.
The Lost and Found quest requires you to kill 50 enemies in each of three locations in the Dreadnaught: the Hull Breach, Hall of Souls, and the Mausoleum. To do this, you must unlock the Dreadnaught Patrol option by completing the Taken King story missions. When that's done, you will need to kill bosses in the Court of Oryx until the Tech Witch Brooch drops. After you have that quest item in your possession, go back to the Reef and talk to Petra to get your new Exotic.
If the Boolean Gemini doesn’t appear, check your Queen's Wrath ranking on the quest screen. You need to be Rank 3 or higher to get the Exotic Scout Rifle. If you're coming up short, you can complete some of the bounties Petra provides when you talk to her, or head over to the abandoned quests kiosk near Cayde-6, Ikora, and Zavala and redo the House of Wolves quest line.