If angles A,B and C are in AP, then (a+c)b is equal to
2sin(A–C)2
2cos(A–C)2
cos(A–C)2
sin(A–C)2
Explanation for the correct option:
Step 1. Find the value of (a+c)b:
Given, A,B and C are in AP.
⇒2B=A+C
⇒ B=(A+C)2 …(i)
As We know,
asinA=bsinB=csinC=k
a=ksinA
b=ksinB
c=ksinC
Step 2. Put the values of a,b,c in given expression:
∴(a+c)b=(ksinA+ksinC)ksinB=(sinA+sinC)sinB=2sin(A+C)2cos(A–C)2sinB=2sin(A+C)2cos(A–C)2sin(A+C)2=2cos(A–C)2 ∵sinθ+sinϕ=2sin(θ+ϕ)2cos(θ+ϕ)2
Hence, Option ‘B’ is Correct.
If a,b,c,d,e,f are in AP then e - c is equal to what?