If In`(a+c),ln(a-c),ln(a-2b+c)` are in `AdotPdot,` then

If the sides a , b and c of A B C are in AdotPdot, prove that 2sinA/2sinC/2=sinB/2

In triangle A B C , if cotA ,cotB ,cotC are in AdotPdot, then a^2,b^2,c^2 are in ____________ progression.

If a. b, c are in G.P. and log_ca , log_b c , log_a b are in AP show that the common difference of the AP is 1(1/2)

Suppose A, B, C are defined as A=a^2b+a b^2-a^2c-a c^2 , B=b^2c+b c^2-a^2b-a b^2 - bc^2, and C=a^2c +'a c^2-b^2' c-b c^2, w h e r ea > b > c >0 and the equation A x^2+B x+C=0 has equal roots, then a ,b ,c are in AdotPdot b. GdotPdot c. HdotPdot d. AdotGdotPdot

Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while log ((5c)/(2a)), log((7b)/(5c)), log((2a)/(7b)) are in A.P. Then a, b, c are the lengths of the sides of

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b^2+bc+c^2).y^(c^2+ca+a^2).z^(a^2+ab+b^2)=1

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then prove that x^(b+c).y^(c+a).z^(a+b) = 1

If (log x)/(b-c) = (log y)/(c-a) = (log z)/(a-b) , then which of the following is/are true?

If A,B,C, are the angles of a triangle such that cot(A/2)=3tan(C/2), then sinA ,sinB ,sinC are in (a) AdotPdot (b) GdotPdot (c) HdotPdot (d) none of these

int(ln(tanx)/(sinxcosx)dx is equal to (a) 1/2ln(tanx)+c (b) 1/2ln(tan^2x)+c (c) 1/2(ln(tanx))^2+c (d) none of these