Mathematics · 2024
JEE Main · 31 January 2024, Shift 2 · Q20
If a= sin^-1( sin (5)) and b= cos^-1( cos (5)), then a^2+b^2 is equal to
If $\displaystyle a=\sin ^{-1}(\sin (5))$ and $\displaystyle b=\cos ^{-1}(\cos (5))$, then $\displaystyle a^2+b^2$ is equal to
Official answer
From NTA’s final answer key for this paper.
(4)
$\displaystyle 8 \pi^2-40 \pi+50$
More from Inverse Trigonometric Functions
- Let [x] denote the greatest integer less than or equal to x. Then the domain of f(x)= sec^-1(2[x]+1) is:2025
- If (π)/4+Σ_p=1^11 tan^-1((2^p-1)/(1+2^2 p-1))=α, then tan α is equal to ____.2026
- If (π)/2 ≤ x ≤ (3 π)/4, then cos^-1(12/13 cos x+5/13 sin x) is equal to2025
- Considering the principal values of the inverse trigonometric functions, sin^-1((√3)/2 x+1/2 √(1-x^2)),-1/2<x<1/(√2), is equal to2025
- Let x=m/n ( m, n are co-prime natural numbers) be a solution of the equation cos (2 sin^-1 x)=1/9 and let α, β(α>β) be the roots of the equation m…2024
- Given that the inverse trigonometric function assumes principal values only. Let x, y be any two real numbers in [-1,1] such that cos^-1 x- sin^-1…2024
- Let α=3 sin^-1(6/11) and β=3 cos^-1(4/9), where inverse trigonometric functions take only the principal values. Given below are two statements:…2026
- Let the maximum value of ( sin^-1 x)^2+( cos^-1 x)^2 for x ∈[-(√3)/2, 1/(√2)] be m/n π^2, where gcd(m, n)=1. Then m+n is equal to ____.2026
JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.