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Prove that cos(sin A) > sin(cos A) for all A in the set [0,π/2]

Prove that cos(sin A) > sin(cos A) for all A in the set [0,π/2]

Grade:11

1 Answers

Arun
25763 Points
4 years ago
We know that
sin A+ cos A \sqrt2   (a sinx+ b cosx \sqrt(a2+b2)
sin A+ cos A \pi/2
sin A \pi/2 –cos A
taking cos both the sides
cos(sin A) > cos(\pi/2 –cosA)       (inequality sign changes because on icreasing angle , cos value will decrease)
cos(sin A) > sin(cos A)
hence proved

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