For θ∈[0,π], let f(θ)=sin(cosθ) and g(θ)=cos(sinθ). Let a=max0≤θ≤πfθ,b=min0≤θ=πfθ,c=max0≤9≤πgθ and d=min0

Question

For θ∈[0,π], let f(θ)=sin(cosθ) and g(θ)=cos(sinθ). Let a=max0≤θ≤πfθ,b=min0≤θ=πfθ,c=max0≤9≤πgθ and d=min0<θ<πgθ. The correct inequalities satisfied by a, b, c, d are

MARKS Content Team · Accepted Answer

Correct answer: (C) b<d<a<c. f(θ)=sin(cosθ) g(θ)=cos(sinθ) f^(')(θ)=cos(cosθ)(-sinθ)<0∀θ∈[0,π] ∴f(θ) decreases monotonically ∴a=maxf(θ)=f(0)=sin1 b=minf(θ)=f(π)=-sin1 g^(')(θ)=-sin(sinθ)cosθ g(θ)=1;g(π)=1;g(π)/2=cos1 ∴c=maxg(θ)=1 d=ming(θ)=cos1 ∴b<d<a<c

For $θ \in [0, π],$ let $f (θ) = \sin (\cos θ)$ and $g (θ) = \cos (\sin θ) .$ Let $a = \max_{0 \leq θ \leq π} f (θ), b = \min_{0 \leq θ = π} f (θ), c = \max_{0 \leq 9 \leq π} g (θ)$ and $d = \min_{0 < θ < π} g (θ) .$ The correct
inequalities satisfied by $a, b, c, d$ are

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