Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Advanced
Exam
JEE Advanced
Subject
Mathematics
Chapter
Trigonometry

JEE Advanced · Mathematics · Trigonometry

Given A= ^2 θ( ^2 θ+1)+2 ^2 θ . Then for all θ,[A] can assume...

Given A=cos⁡2θ(cos⁡2θ+1)+2sin⁡2θA=\cos ^2 \theta\left(\cos ^2 \theta+1\right)+2 \sin ^2 \theta. Then for all θ,[A]\theta,[A] can assume values whose sum is ______ (Where [.] denotes the greatest integer function).

Correct answer

3

Step-by-step solution

 On solving we have A=cos⁡4θ+1−cos⁡2θ+1=(cos⁡2θ−12)2+74⇒A∈[74,2]\text { On solving we have } A=\cos ^4 \theta+1-\cos ^2 \theta+1=\left(\cos ^2 \theta-\frac{1}{2}\right)^2+\frac{7}{4} \Rightarrow A \in\left[\frac{7}{4}, 2\right]
Practice Trigonometry on Quantrex Academy →

More from Trigonometry

The number of real root(s) of the equation x^2 x=1 lie(s) between 0 and 2 π is/are Most Important Selected Qs for JEE AdvancedIf |x^2-(π)/(4)+ x-2|=|x^2-2|+| x|+(π)/(4) then Most Important Selected Qs for JEE AdvancedIf 3 x+ (2 x-(7 π)/(6))=-2 , then x is equal to ( where m ∈ I) Most Important Selected Qs for JEE AdvancedWhat is the minimum value of ( ^4 α)/( ^2 β)+( ^4 β)/( ^2 α) for α, B ≠ (k π)/(2), k ∈ Z ? Most Important Selected Qs for JEE AdvancedIf x+ y ≥ α x x ∈ R then y+ α is equal to Most Important Selected Qs for JEE AdvancedIf A, B are the roots of the quadratic equation a b x^2-c^2 x+a b=0 where a, b, c are… Most Important Selected Qs for JEE AdvancedIf θ and - θ are the roots of the equation a x^2-b x-c=0 , where a, b, c are the sides of… Most Important Selected Qs for JEE AdvancedIf 2 ^2((π)/(2) ^2 x)=1- (π 2 x), x ≠(2 n+1) (π)/(2), n ∈ I , then Most Important Selected Qs for JEE AdvancedConsider the equation 1+ 3 2 x ^4 x+4 ^2 x + ^4 x+4 ^2 x = 2 ^ -1 ( 2 x) x ∈(-π, π) Most Important Selected Qs for JEE AdvancedSet of values of x of the equation 2 x= ( ^3 x- ^3 x) is - Most Important Selected Qs for JEE AdvancedIf 4+ 8- 32+ 768 =a 2 \ left((11 π)/(b)), where a and b are natural numbers then (b)/(a)… Most Important Selected Qs for JEE AdvancedIf a x+ x+1=cosec x then the possible values of x can be Most Important Selected Qs for JEE AdvancedFor the equation 2( x- 2 x)- 2 x(1+2 x)+2 x=0, x ∈[0,2 π]- Most Important Selected Qs for JEE AdvancedWhich of the following set of values of x satisfies the equation 2^ (2 ^2 x-3 x+1) +2^… Most Important Selected Qs for JEE AdvancedIf α satisfies the equation 2 2 ^3 x-54 2 ^3 x=19 , then possible value of ( .2 ^2 α+ 2… Most Important Selected Qs for JEE AdvancedIf f(x)=(3)/(1+ ^2 x)+(9)/(1+ ^2 x) , then : Most Important Selected Qs for JEE Advanced Full Trigonometry list Trigonometry JEE Maths PYQsJEE Mathematics PYQs All Most Important Selected Qs for JEE Advanced PYQs