If cosec⁡A+sec⁡A=cosec⁡B+sec⁡B then tan⁡Atan⁡B is equal to

sec⁡A−sec⁡B=cosec⁡B−cosec⁡A⇒ cos⁡B−cos⁡Acos⁡Acos⁡B=sin⁡A−sin⁡Bsin⁡Asin⁡B⇒ sin⁡Asin⁡Bcos⁡Acos⁡B=sin⁡A−sin⁡Bcos⁡B−cos⁡A⇒ tan⁡Atan⁡B=2cos⁡A+B2sin⁡A−B22sin⁡A+B2sin⁡A−B2=cot⁡A+B2