If maximum and minimum values of
begin mathsize 20px style open vertical bar table row cell 1 plus cos squared x space space end cell cell sin squared x end cell cell cos 2 x end cell row cell cos squared x end cell cell 1 plus sin squared x space space end cell cell cos 2 x end cell row cell cos squared x end cell cell sin squared x end cell cell 1 plus cos 2 x end cell end table close vertical bar space a r e space alpha space a n d space beta space r e s p e c t i v e l y comma t h e n
i. space alpha squared plus beta to the power of 101 equals 10 space space space space space space i i. space alpha cubed minus beta to the power of 99 equals 26 space space space space i i i. space 2 alpha squared minus 18 beta to the power of 11 equals 0 space space space i v. space a l l space o f space t h e s e end style

Asked by sunil2791 | 8th Jul, 2017, 07:44: PM

Expert Answer:

begin mathsize 16px style
open vertical bar table row cell 1 plus cos squared straight x end cell cell sin squared straight x end cell cell cos 2 straight x end cell row cell cos squared straight x end cell cell 1 plus sin squared straight x end cell cell cos 2 straight x end cell row cell cos squared straight x end cell cell sin squared straight x end cell cell 1 plus cos 2 straight x end cell end table close vertical bar
straight R subscript 1 rightwards arrow straight R subscript 1 minus straight R subscript 3 comma space straight R subscript 2 rightwards arrow straight R subscript 2 minus straight R subscript 3
open vertical bar table row 1 0 cell negative 1 end cell row 0 1 cell negative 1 end cell row cell cos squared straight x end cell cell sin squared straight x end cell cell 2 cos squared straight x end cell end table close vertical bar..................... left parenthesis 1 plus cos 2 straight x equals 2 cos squared straight x right parenthesis
solving space this space we space get
2 cos squared straight x plus 1
1 plus 2 cos squared straight x
1 plus 1 plus cos 2 straight x
2 plus cos 2 straight x
Consider comma
minus 1 less or equal than cos 2 straight x less or equal than 1
2 minus 1 less or equal than 2 plus cos 2 straight x less or equal than 2 plus 1
1 less or equal than 2 plus cos 2 straight x less or equal than 3
maximum space value equals straight alpha equals 3
Minimum space value equals straight beta equals 1
If space we space put space it space in space all space the space options space we space will space get space answer space as
all space of space these.

end style

Answered by Sneha shidid | 8th Jul, 2017, 11:48: PM