KVPY SX SB Exam 2016 Question Paper

Question : 9 of 120

Marks: +1, -0

X = {x ∈ R : cos (sin x) = sin (cos x)}. The number of elements in X is -

Solution:

cos (sin x) = sin (cos x)

\sin(π/2±\sin x)=\sin(\cos x)

\cos x=nπ+(-1)^n(π/2+\sin x),

n ∈I

⇒\cos x±\sin x=nπ+(-1)^n\;\;π/2,

n ∈I

As LHS

∈ [ -√ 2, √2 ]

, and it does not satisfies RHS
So No solution possible

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