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in Differential equations by (50.2k points)

Find the max and min values of f(θ) = sin2(sinθ) + cos2(cosθ)

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We have, sin2(sinθ) + cos2(cosθ

= sin2(cosθ) + cos2(cosθ) + sin2(sinθ) – sin2(cosθ

= (sin2(cosθ)+cos2(cosθ)) + sin2(sinθ) – sin2(cosθ)

= 1 + (sin2(sinθ) – sin2(cosθ)) 

Max value of f(θ)

= 1 + (sin2(sin (π/2)) – sin2(cos(π/2)))

= 1 + sin2(1) 

Min value of f(θ) 

= 1 + (sin2(sin(0)) – sin2(cos(0))) 

= 1 – sin2(1)

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