Question

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. 1
D. `sqrt(3)`

Answer 1

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)`