Question

If c o t a + 2 t a n a = t a n b then c o t a is

Answer 1

Hey,


2TanA+CotA=TanB
we will substitute this value of TanB  while solving the answer.
CotA + 2Tan(A-B) 
= CotA + 2 [ (TanA-TanB)/ (1+TanATanB)]
= CotA + 2 [ ​(TanA-2TanA-CotA)/ (1+TanA(2Tan+CotA))]
= CotA + 2 [(-TanA-CotA)/(1+2Tan2A+1)]
= CotA + 2 [​(-TanA-CotA)/(2+2Tan2A)]
= ​ CotA + [​(-TanA-CotA)/(1+Tan2A)]
=  ​​ CotA + [​(-TanA-CotA)/(Sec2A)]
=  CotA - TanA/Sec2A - CotA/​Sec2A

= CotA - SinACosA - CotACos2A
= CotA(1-Cos2A) - SinACosA
=  CotA(Sin2A) - SinACosA
=  SinACosA - SinACosA
=  0
therefore CotA + 2Tan(A-B) = 0 

HOPE IT HELPS YOU:-))

Answer 2

Answer:

Hey guys pls check your answer