This is a Test of Mathematics Solution Subjective 79 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.

Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta

## Problem

Let , , … , be any values in the closed interval . Show that

= \( {(1 + {\sin}^2 \theta_1)(1 + {\cos}^2 \theta_1)(1 + {\sin}^2 \theta_2)(1 + {\cos}^2 \theta_2)………(1 + {\sin}^2 \theta_{10})(1 + {\cos}^2 \theta_{10})} \) .

What is the maximum value attainable by and at what values of , , … , , is the maximum value attained?

## Solution

=

Now we will show that for any

Now

[ as ]

So for any

So (proved)

Maximum value attained by is and will be attained for for