Let f θ = 1 1 + tan ⁡ θ 2021 , then the value of ∑ θ = 1 ° 89 ° f θ is equal to

Question

Let f θ = 1 1 + tan ⁡ θ 2021 , then the value of ∑ θ = 1 ° 89 ° f θ is equal to, 45, 44, 89 2, 91 2

MARKS App · Accepted Answer

f θ = cos ⁡ θ 2021 sin ⁡ θ 2021 + cos ⁡ θ 2021 f 90 ° - θ = sin ⁡ θ 2021 cos ⁡ θ 2021 + sin ⁡ θ 2021 ⇒ f θ + f 90 ° - θ = 1 and f 45 ° = 1 2 Hence, ∑ θ = 1 o 89 o f θ = f 1 o + f 2 o + … + f 44 o + f 46 o + … + f 88 o + f 89 o + f 45 o = f 1 o + f 89 o + f 2 o + f 88 o + … + f 44 o + f 46 o + f 45 o = 1 × 44 + 1 2 = 89 2

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