Question

If the angles A,B and C of a triangle are in arithmetic
progression and if a,b and c denote the sides opposite to A, B and C respectively, then the value of the expression

(a/c)Sin2C + (c/a)Sin2A is

Answer 1

\[
\sin^2(C)
\]or \[
\sin(2C)
\]

Answer 2

The latter

Answer 3

Arithmetic progression just means:\[
B-A=C-B
\]

Answer 4

Yes

Answer 5

This might help:\[
\frac{a\sin2C}{c}=\frac{a2\sin C\cos C}{c}=\frac{a2\sin A\cos C}{a} = 2\sin A\cos C
\]

Answer 6

Yes it has to do with the Sine and Cosine rule

Answer 7

By symmetry, they both end up being the same thing, resulting in:\[
4\sin A\cos C
\]

Answer 8

Wait that is wrong.

Answer 9

\[
2\sin A\cos C+2\sin C\cos A
\]

Answer 10

I found that in a IIT-jee paper

Answer 11

i mean question

Answer 12

Its the most difficult question in that paper they say

Answer 13

We should probably use the \[
C=2B-A
\]

Answer 14

You continue to use angle formula

Answer 15

One thing we could do is just say \[
A=30^\circ, B=60^\circ, C=90^\circ
\]

Answer 16

Wait i got to go. I think i will figure it out by tommorow and yes B=60 degrees