Show that in a <mi mathvariant="normal">&#x0394;<!-- Δ --> A B C , sin &#x2061;

cdsommegolfzp

cdsommegolfzp

Answered question

2022-07-01

Show that in a Δ A B C, sin A 2 a b + c
Hence or otherwise show that csc n A 2 + csc n B 2 + csc n C 2 has the minimum value 3.2 n for all n 1

Answer & Explanation

Alisa Jacobs

Alisa Jacobs

Beginner2022-07-02Added 13 answers

1 sin x 2 is a convex function over I = ( 0 , π ) as well as ( 1 sin x 2 ) n since it is positive and log-convex:
d 2 d x 2 ( log sin ( x / 2 ) ) = 1 4 csc 2 x 2 .
The claim hence follows from Jensen's inequality.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?