IIT JEE , AIEEE Forum - Mathematics , Algebra

gaurav_2351

IN TRIANGLE ABC tanA/2=5/6

tanB/2= 2/5

THEN FIND CORRECT ORDER OF ARITHMETIC PROGRESSION OF a,b,c

Avinash_Bhat

Given : tan(A/2) = 5 / 6
tan(B/2) = 2 / 5

In a triangle:

tan(A/2) tan(B/2) + tan(B/2) tan(C/2) + tan(C/2) tan(A/2) = 1

So tan(C/2) = 20 / 37

We know that : sin 2

= 2 tan

/ ( 1 + tan²

)

sin A = 20 / 29
sin B = 60 / 61
sin C = 1480 / 1769

We also have:

a / sin A   =   b / sin B   =   c / sin C   = k(non-zero constant)

a = ksin A = k (20 / 29)
b = ksin B = k (60 / 61)
c = ksin C = k (1480 / 1769)

But:

2 (1480 / 1769) =   (20 / 29) + (60 / 61)

2 (c / k)   =   (a / k) + (b / k)

2c = a + b

                                                                a , c , b are in A.P.

                                                                          AND

                                                                b , c , a are in A.P.

ayshwarya

hi avinash no need of using such long method remember dis
TAN A/2 XTAN B/2=a+b-c/a+b+c
similarly fr TAN B/2 x TAN C/2 =b+c-a/b+c+a
similarly fr tan A/2 xtan C/2 also
dis is a short cut & will help in competitive exams as well fr fast solvation

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