I am having a very similar problem trying to thether my Ipad 3 running iOS 7.1 to my Mac Book Pro running OSX 10 .9.2.
I tried the suggestion using the Disk Utility then rebooted Mac, started Itunes , then unlocked the Ipad, and connected the USB. The same problem appears.... the Ipad flashes the "Trust This Commputer" popup, but too fast to respond.
The error message from the console on the mac book pro is
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _receive_message (thread 0x100787000): Far end closed connection: Undefined error: 0
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: device_os_is_at_least (thread 0x100787000): AMDeviceConnect failed: 0xe8000084
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _send_message (thread 0x100787000): Could not send message size 377: Broken pipe.
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _AMDevicePreflightWorker (thread 0x100787000): Pair worker could not pair with device 133: 0xe8000084
Apr 19 16:16:29 terrys-mbp.gateway iTunes[289]: Entered:_AMMuxedDeviceDisconnected, mux-device:134
Apr 19 16:16:29 terrys-mbp.gateway iTunes[289]: Entered:__thr_AMMuxedDeviceDisconnected, mux-device:134
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _receive_message (thread 0x100787000): Far end closed connection: Undefined error: 0
Apr 19 16:16:29 terrys-mbp.gateway iTunes[289]: tid:1572b - Mux ID not found in mapping dictionary
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: device_os_is_at_least (thread 0x100787000): AMDeviceCopyValueWithError: 0xe8000084
Apr 19 16:16:29 terrys-mbp.gateway iTunes[289]: tid:1572b - Can't handle disconnect with invalid ecid
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _send_message (thread 0x100787000): Could not send message size 377: Broken pipe.
Apr 19 16:16:29 terrys-mbp.gateway usbmuxd[45]: _AMDevicePreflightWorker (thread 0x100787000): Pair worker could not pair with device 134: 0xe8000084
Apr 19 16:16:30 terrys-mbp.gateway iTunes[289]: Entered:_AMMuxedVersion2DeviceConnected, mux-device:135
Apr 19 16:16:30 terrys-mbp.gateway iTunes[289]: tid:19747 - unable to query device capabilities