1.

The ratio of the greatest value of `2-cos x+s in^2x`to its least value is`7/4`(2) `9/4`(3) `(13)/4`(4) `5/4`A. `7/4`B. `11/4`C. `13/4`D. none of these

Answer» Correct Answer - C
Let `y=2-cosx+sin^(2)x.Then,`
` y=2-cosx+1-cos^(2)x`
`impliesy=3-(cos^(2)x+cos)impliesy=13/4-(cosx+1/2)^(2)`
Now, `-1lecosx le1` for all x
`implies-1/2le(cosx+1/2)^(2)lt0"for all x"`
`implies13/4-9/4le13/4(cosx+1/2)^(2)le13/4"for all x"`
`implies1ley13/4`
`thereforey_(max)=13/4and y_(min)=1`
Hence, required ratio is `13/4`


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