If `A,A_(1),A_(2),A_(3)` are the areas of incircle and ex-circle of a triangle respectively then prove that `(1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))=(1)/(sqrt(A))`

If A, A_(1),A_(2),A_(3) are areas of excircles and incircle of a triangle, then (1)/(sqrt(A_(1)))+(1)/(sqrt(A_(2)))+(1)/(sqrt(A_(3)))=

If a_(1), a_(2), a_(3),…..a_(n) are in A.P where a_(i) gt 0, AA I then (1)/(sqrt(a_(1)) + sqrt(a_(2))) + (1)/(sqrt(a_(2)) + sqrt(a_(3)))+ …+ (1)/(sqrt(a_(n-1)) + sqrt(a_(n))) = (k)/(sqrt(a_(1)) + sqrt(a_(n))) then k=

If a_(1), a_(2) …… a_(n) are in A.P then (sqrt(a_(1)) + sqrt(a_(n)))/( sqrt(a_(1)) + sqrt(a_(2))) + (sqrt(a_(1)) + sqrt(a_(n)))/(sqrt(a_(2)) + sqrt(a_(3))) + ….. + (sqrt( a_(1)) + sqrt(a_(n)))/( sqrt(a_(n - 1)) + sqrt(a_(n))) =

Let A_(0)A_(1)A_(2)A_(3)A_(4)A_(5) be a regular hexagon inscribed in acircle of unit radius. Then the product of the length of the line segments A_(0)A_(1),A_(0)A_(2)andA_(0)A_(4) is

If the coefficients of 4 consecutive terms in the expansion of (1+x)^(n) are a_(1),a_(2),a_(3),a_(4) respectively, then show that (a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

If a_(1), a_(2), a_(3), a_(4) are the coefficients of the 2^(nd), 3^(rd), 4^(th) and 5^(th) terms respectively in the binomial expansion of (1+x)^(n) where n is a positive integer prove that (a_(1))/(a_(1)+a_(2)) , (a_(2))/(a_(2)+a_(3)) , (a_(3))/(a_(3)+a_(4)) are in arithmetic progression.

f:AtoA,A={a_(1),a_(2),a_(3),a_(4),a_(5)} , the number of one one functions so that f(x_(i))nex_(1),x_(i)inA is

If a_(1),a_(2),a_(3),....,a_(n) is an A.P. with common difference d, then tan[Tan^(-1)(d/(1+a_(1)a_(2)))+Tan^(-1)(d/(1+a_(2)a_(3)))+...Tan^(-1)(d/(1+a_(n-1)a_(n)))=

If a_(1),a_(2),a_(3),...a_(n) are in A.P. with common difference d, then tan[tan^(-1)((d)/(1+a_(1)a_(2)))+tan^(-1)((d)/(1+a_(2)a_(3)))+,....+tan^(-1)((d)/(1+a_(n-1)a_(n)))]=