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

Question

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

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Answer 1 · 2018-06-13T14:54:51

Answer for the question.

How can I solve this problem

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

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.