1+tanhx21-tanhx2isequalto
e-x
ex
2ex/2
2e-x/2
Explanation for the correct option:
Solve the given expression using identities
1+tanhx21-tanhx2 =1+sinhx2coshx21-sinhx2coshx2
=sinhx2​+coshx​2coshx2​−sinhx2​
=​ex2​e-x2=ex ∵sinhx2+coshx2=ex2,coshx2-sinhx2=e-x2
Hence, Option ‘B’ is Correct.
Let [k] denotes the greatest integer less than or equal to k. Then the number of positive integral solutions of the equation [x[π2]]=⎡⎢ ⎢⎣x[1112]⎤⎥ ⎥⎦ is