UPSEE Solved Model Paper 3

Let f (θ) = cos2 (cos θ) + sin2 (sin θ)
Since - 1 ≤ cos θ ≤ - 1 and - 1 ≤ sin θ ≤ 1
∴ cos 1 ≤ cos (cos θ) ≤ 1 and - sin 1 ≤ sin (sin θ) ≤ sin 1
∴ cos21 ≤ cos2(cosθ) ≤ 1 and 0 ≤ sin2(sinθ) ≤ sin211
∴ Maximum value = 1+sin21