If `y=cos^2theta+sin^4theta` then for all real values of `theta`

Options

A. `y in[1,2]`
B. `yin[13//16,1]`
C. `y in[3//4,13//16]`
D. `y in[3//4,1]`

Answer

D

Explanation

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`