0

Guest

Courses New

if ∑(tan2 r-1 )/(cos2 r )= tanp n – ​tanq, then find the value of p+q

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

Grade:11

2 Answers

Aditya Gupta
2081 Points
4 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
13 Points
3 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
.
.
.
FINAL ANSWER TAN(2^N)-TAN(2^n-1) / TAN 2N-TAN1
 

Think You Can Provide A Better Answer ?

Other Related Questions on Trigonometry

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More