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if ∑(tan2r-1)/(cos2r)= tanpn – ​tanq,
then find the value of p+q

Abhinandan Angra , 6 Years ago
Grade 11
anser 2 Answers
Aditya Gupta

Last Activity: 5 Years ago

write tan2r-1= tan(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 :))

Aiyatullah Saiyed

Last Activity: 4 Years ago

tan(2^0)/cos2+....tan(2^n-1)/cos^2n
Apply the formula splitting the sum by replacing x=2^n
it gives tan(2^n)-tan 1
 
TAN(1) SEC(2)=TAN2-TAN1
TAN(2) SEC(2^2)=TAN(2^2)-TAN1
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.
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FINAL ANSWER TAN(2^N)-TAN(2^n-1) / TAN 2N-TAN1
 

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