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1)

coth1(3)+tanh113cosech1(3)=


A) loge(23)

B) loge23

C) 0

D) loge33

Answer:

Option B

Explanation:

 We know that ,  coth1x=12loge(x+1x1),|x|>1

 tanh1x=12loge(1+x1x)

and   cosech1x=loge(11+x2x),x<0

       coth1(3)=12loge(42)=loge2

 tanh1(13)=12loge(1+1/311/3)=12loge(42)=loge2

 and     cosech1(3)=loge(11+33)

   =   loge(123)=loge(13)

 Hence,   coth1(3)+tanh113cosech1(3)=

 = loge2+loge2loge(13)

 =loge(2.2)+loge(3)=loge(23)