equation

if x is real then prove that the expression
(x²-2xcos2Î¸+1)/(x²-2xcos2Ï†+1)
lies btween sin²Î¸/sin²Ï† and cos²Î¸/cos²Ï†.

1 Answers

1357

Manish Shankar ·2009-08-07 22:17:56

Let (x²-2xcos2Î¸+1)/(x²-2xcos2Ï†+1)=m
then
(x²-2xcos2Î¸+1)=m(x²-2xcos2Ï†+1)
or x²-2x{mcos2Ï†-cos2Î¸}/(m-1) +1=0

put discriminantâ‰¥0 and you will get what you want

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