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Grade: 11
        
if ∑(tan2r-1)/(cos2r)= tanpn – ​tanq,
 
then find the value of p+q
one year ago

Answers : (1)

Aditya Gupta
1905 Points
							
write tan2r-1tan(2r/2)= (1 – cos2^r)/sin2^r
so, (tan2r-1)/(cos2r)= 2/(2sin2^rcos2^r) – 1/sin2^r
=1/sin2^(r+1) + [1/sin2^(r+1) – 1/sin2^r]
[1/sin2^(r+1) – 1/sin2^r] is telescopic.
for 1/sin2^(r+1) = 1/(2sin2^rcos2^r), note that
1/sinxcosx= 2(cotx – cot2x)
so, 1/(2sin2^rcos2^r)= cot2^r – cot2^(r+1), which again telescopes!
KINDLY APPROVE :))
28 days ago
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