In a triangle, if r1+r3=kcos2B2,then k is equal to:
R
2R
3R
4R
Determine the value of k
Calculating r1+r3:
: r1=4RsinA2cosB2cosC2r3=4RcosA2cosB2sinC2addingr1andr3,wegetr1+r3=4RsinA2cosB2cosC2+4RcosA2cosB2sinC2=4RcosB2sinA2cosC2+cosA2sinC2=4RcosB2sinA+C2=4RcosB2sin180°-B2r1+r3=4Rcos2B2Comparingwithr1+r3=kcos2(B2)[Given]∴k=4R
Hence, Option (D) is correct.