If `x=cos^2theta+sin^4theta` then for all real values of `theta`A. `y – InterviewSolution

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1.	If `x=cos^2theta+sin^4theta` then for all real values of `theta`A. `y in[1,2]`B. `yin[13//16,1]`C. `y in[3//4,13//16]`D. `y in[3//4,1]`
Answer» Correct Answer - D We have, `y-sin^(2)theta+cos^(4)theta` `impliesy=cos^(4)theta-cos^(2)theta+1` `impliesy=(cos^(2)theta-(1)/(2))^(2)+3/4` Now, `0le cos^(2)theta-1/2le 1/2` `implies0le(cos^(2)theta-1/2)^(2)+3/4le1implies3/4leyle1`

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