* 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