The correct option is C 2RcosAcosBcosC
We know, sides of the pedal triangle are acosA,bcosB,ccosC.
Now, acosA=2RsinAcosA=Rsin2A
Area of pedal triangle is Δp=12DE.DF.sin(∠EDF)=12(Rsin2B)(Rsin2C)sin(180∘−2A)=12R2sin2Asin2Bsin2C
Now, semi perimeter is Sp=12(Rsin2A+Rsin2B+Rsin2C)=R2(sin2A+sin2B+sin2C)=2RsinAsinBsinC
Hence inradius rp=ΔpSp=Rsin2Asin2Bsin2C4sinAsinBsinC⇒rp=2RcosAcosBcosC