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)