If the angle `A ,Ba n dC`of a triangle are in an arithmetic propression and if `a , ba n dc`denote the lengths of the sides opposite to `A ,Ba n dC`respectively, then the value of the expression `a/csin2C+c/asin2A`is`1/2`(b) `(sqrt(3))/2`(c) `1`(d) `sqrt(3)`A. `(1)/(2)`B. `(sqrt(3))/(2)`C. 1D. `sqrt(3)`

If the angle `A ,Ba n dC`of a triangle are in an arithmetic propressio

1.	If the angle `A ,Ba n dC`of a triangle are in an arithmetic propression and if `a , ba n dc`denote the lengths of the sides opposite to `A ,Ba n dC`respectively, then the value of the expression `a/csin2C+c/asin2A`is`1/2`(b) `(sqrt(3))/2`(c) `1`(d) `sqrt(3)`A. `(1)/(2)`B. `(sqrt(3))/(2)`C. 1D. `sqrt(3)`
Answer» Correct Answer - D Since A,B,C are in AP `rArr 2B=A+C i.e., angle B =60^(@)` `:. (a)/(c)(2 sin C cos C)+(c)/(a)(2 sin A cos A)` `=2k(a cos C+c cos A)` [ Using `(a)/(ainA)=(b)/(sinB)=(c)/(sinC)=(c)/(sin C)=(1)/(k)]` `=2k(b)` `=2 sin B " " [ "using" b=a cos C+c cos A]` `=sqrt(3)`