If sinh-1(2)+sinh-1(3)=x, then coshx is equal to
12[35+210]
12[35–210]
12[12+250]
12[12–250]
Step1. Applying given condition :
Given sinh-1(2)+sinh-1(3)=x
We now that sinh-1(x)=ln[x+x2+1]
Then sinh-1(2)+sinh-1(3)=ln[2+4+1]+ln[3+9+1]
=ln(2+5)+ln(3+10)=ln[(2+5)(3+10)]=x
Step2. Find the value of coshx:
Now, coshx=(ex+e-x)2
=eln[(2+5)(3+10)]+e-ln[(2+5)(3+10)]2=12(2+5)(3+10)–1(2+5)(3+10)
On further simplification we get,
Hence, the correct option is (C).
If x2−hx−21=0 , x2−3hx+35=0 (h>0) has a common root, then the value of h is equal to