How can I solve this problem #cot(a-45)= (1+tan(a))/tan(a)-1#?

#cot(alpha-45^circ)=(1+tanalpha)/(tanalpha-1)#

1 Answer
Jun 13, 2018

Answer for the question.

How can I solve this problem

#cot(alpha-45^circ)=(1+tanalpha)/(color(red)(tanalpha-1)#

Explanation:

We have to prove:

#cot(alpha-45^circ)=(1+tanalpha)/(tanalpha-1)#

We know that,

#color(red)(cot(A-B)=(cotAcotB+1)/(cotB-cotA}#

Let, #A=alpha and B=45^circ#

#=>cot(alpha-45^circ)=(cotalphacot45^circ+1)/(cot45^circ-cotalpha)#

#=>cot(alpha-45^circ)=(cotalpha*1+1)/(1-cotalpha)...to[becausecot45^circ=1]#

#=>cot(alpha-45^circ)=(1/tanalpha+1)/(1-1/tanalpha)#

#=>cot(alpha-45^circ)=(1+tanalpha)/(tanalpha-1)#

Thus the updated question is proved.