Question

the minimum value of sec^2A + cosec^2A is
a)1
b) -2
c)2
d)4

Answer 1

AM>=GM should help your case

Answer 2

can you explain it more !

Answer 3

(sec^2 a + cosec^2 a) >= 2 seca cosec

this much should be clear ?

Answer 4

so that means \[4+( \tan \theta - \cot \theta)^2 \ge 4 \]

Answer 5

and the minimum value be 4 . m i right ?

Answer 6

how did you get that? :O

Answer 7

\[1 +\tan^2 \theta + 1+ \cot^2 \theta \]

Answer 8

\[2 +(\tan \theta -\cot \theta )^2 + 2 \tan \theta .\cot \theta \]

Answer 9

what after that ?

Answer 10

then as you have told me \[4+( \tan \theta - \cot \theta )^2\ge 4\]

Answer 11

how you get 4 on RHS ?

Answer 12

cause simply you get \[4+ (\tan \theta - \cot \theta )^2 \]

Answer 13

which is grearter than 4

Answer 14

ohh.. so you have not used AM>=GM ..oh okay, I wondered how you got that from AM>=GM
hmm
nice
yes, 4 should be the ans

Answer 15

well thank you !

Answer 16

nice :)

Answer 17

another way
sec^2A + cosec^2A

1/cos^2A + 1/sin^2A

sin^2A+ cos^2A
----------------
cos^2A sin^2A

1
-------------
cos^2A sin^2A

4
-----------
sin^2 2A


smallest value = when bottom is large = 4