Question

The Minimum Value of :

\[(\sin x + cosec x )^2 + (\cos x + \sec x)^2\]

Answer 1

My work :


\[\sin^2 x+ 2 + cosec^2 x + \cos^2x + 2 + \sec^2x\]

=\[5 + cosec^2 x + \sec^2 x\]

=\[7 + \cot^2x + \tan^2 x\]

Answer 2

and i am Stuck From here:

Answer 3

5 + 1/sin^2 x + 1/cos^2 x
= 5 + 1/sin^2 x cos^2 x = 5+ 2/sin (2x)

Answer 4

That...was a gud..Idea..) then

Answer 5

now the minimum occurs where sin 2x is at maximum isnt it?

Answer 6

Yes...)

Answer 7

so......7

Answer 8

thxxx...).....that was awesome..brother

Answer 9

welcme

Answer 10

WELL THE MINIMUM of 5+ 2/sin (2x) is 3 when sin 2x =-1

Answer 11

Isnt it @Yahoo! and @him1618

Answer 12

For the eq to be Min the Denominator Shuld be Maximum

Answer 13

MAx Value of Sin =1