Question
If tan θ = √32, the sum of the infinite series
1 + 2(1 - cosθ) + 3(1 - cosθ)2 + 4(1 - cosθ)3+........∞ is
1 + 2(1 - cosθ) + 3(1 - cosθ)2 + 4(1 - cosθ)3+........∞ is
Answer: Option D
:
D
(d)1 + 2(1 - cosθ) + 3(1 - cosθ)2 + 4(1 - cosθ)3+........ to ∞
= (1 - x)−1, [Let (1 - cosθ) = x]
∴ Series = (1 - 1 + cosθ)−2 = sec2θ
= (1 + tan2θ) = 1 + 32 = 52
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:
D
(d)1 + 2(1 - cosθ) + 3(1 - cosθ)2 + 4(1 - cosθ)3+........ to ∞
= (1 - x)−1, [Let (1 - cosθ) = x]
∴ Series = (1 - 1 + cosθ)−2 = sec2θ
= (1 + tan2θ) = 1 + 32 = 52
Was this answer helpful ?
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