Let |M| denote the determinant of a square matrix M . Let g:[0, \frac{\pi}{2}] \to \mathbb{R} be the function defined by g(\theta)=\sqrt{f(\theta)-1}+\sqrt{f(\frac{\pi}{2}-\theta)-1} where f(\theta)=\frac{1}{2}|\table 1 , \sin \theta , 1 ; -\sin \theta , 1 , \sin \theta ; -1 , -\sin \theta , 1 |+|\table \sin \pi , \cos (\theta+\frac{\pi}{4}) , \tan (\theta-\frac{\pi}{4}) ; \sin (\theta-\frac{\pi}{4}) , -\cos \frac{\pi}{2} , \log _{ {\e}}(\frac{4}{\pi}) ; \cot (\theta+\frac{\pi}{4}) , \log _{ {\e}}(\frac{\pi}{4}), \tan \pi | Let {\p}(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function {\g}(\theta) , and {\p}(2)=2-\sqrt{2} . Then, which of the following is/are TRUE ? [JEE Adv 2022 P1]

Functions

Section: Mathematics

Question : 9 of 30

Marks: +1, -0

Let |M| denote the determinant of a square matrix M . Let g:[0,‌

]→ℝ be the function defined by
g(θ)=√f(θ)−1+√f(‌

−θ)−1
where

f(θ)=‌

1	sin‌θ	1
−sin‌θ	1	sin‌θ
−1	−sin‌θ	1

|+|

sin‌π

cos(θ+‌

)

tan(θ−‌

)

sin(θ−‌

)

−cos‌

loge(‌

)

cot(θ+‌

)

loge(‌

)

tan‌π

Let p(x) be a quadratic polynomial whose roots are the maximum and minimum values of the function g(θ) , and p(2)=2−√2 . Then, which of the following is/are TRUE ?

[JEE Adv 2022 P1]

p(‌
3+√2
4
)<0
p(‌
1+3√2
4
)>0
p(‌
5√2−1
4
)>0
p(‌
5−√2
4
)<0

Validate

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