If cot-1(ɑ)=cot-12+cot-18+cot-118+cot-132+…….. upto 100 terms, then ɑ is:
1.03
1.00
1.01
1.02
Find the value of α:
Let us consider R.H.S =cot-12+cot-18+cot-118+cot-132+……..
=∑n=1100cot-12n2=∑n=1100tan-124n2=∑n=1100tan-1(2n+1)–(2n–1)1+(2n+1)(2n–1)=∑n=1100tan-1(2n+1)–tan-1(2n–1)=tan-1201–tan-11=tan-1200202=cot-1101100
⇒ cot-1α=cot-1101100
∴α=1.01
Hence, Option ‘C’ is Correct.