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Q.

If cot-1(α)=cot-12+cot-18+cot-132+….. up to 100 terms, then α is

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a

1.01

b

1.02

c

1.00

d

1.03

answer is A.

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Detailed Solution

cot-1(α)=∑r=1100cot-12r2 =∑r=1100tan-124r2=∑r=1100tan-1(2r+1)-tan-1(2r-1)=tan-1201-tan-11∣=tan-1200202⇒α=101100=1.01

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