arcsech12-arccosech34 equals
loge3(2+ā2)
loge(1+ā3)3
loge(2+ā3)3
loge(2-ā3)3
Explanation for the correct option:
Step 1. Find the value of given expression:
As we know,
arcsech(x)=ln[1+(1āx2)]x ā¦..(1)
arccosech(x)=ln[1+(x2+1)]x ā¦..(2)
Step 2. Put the value x=12 in equation (1):
sech-112=ln1+1ā1412=ln21+ā32=ln(2+ā3)=loge(2+ā3)
Step 3. Put the value x=34 in equation (2):
cosech-134=ln1+342+134=ln431+916+1=ln431+14(9+16)=ln43+ā253=ln(4+5)3=ln93=ln3=loge3
ā“arcsech12-arccosech34=loge(2+ā3)āloge3=loge[(2+ā3)3] ā¦āµlogea-logeb=loge(ab)
Hence, Option āCā is Correct.