If $a=\sin^{-1}(\sin(5))$ and $b=\cos^{-1}(\cos(5))$, then $a^2+b^2$ is equal to

JEE Main 2024 · MathsMultiple choiceSingle correctMediumCalculation

JEE Main 31 January 2024, Shift 2, Maths Q20

Question 20 of 90 in this shift, Maths question 20 of 30, Section A.

a=\sin^{-1}(\sin(5))

and

b=\cos^{-1}(\cos(5))

, then

a^2+b^2

is equal to

(1)25
(2) $4\pi^2+25$
(3) $4\pi^2-20\pi+50$
(4) $8\pi^2-40\pi+50$ Official answer

Official answer

Option 4

NTA final key.

Chapter: Inverse Trigonometric Functions
Topic: Inverse Trig Identities
Idea tested: Periodic Reduction of sin-1(sin x) and cos-1(cos x)

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Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.