Grade 11Trigonometry
tan1/(1+tan1)+tan2/(1+tan2)+tan3/(1+tan3) ....................... tan88/(1+tan88)+tan89/(1+tan89) = ?
tan1/(1+tan1)+tan2/(1+tan2)+tan3/(1+tan3) ....................... tan88/(1+tan88)+tan89/(1+tan89) = ?
1 Answer
Aditya Gupta
Approved Tutor Answer6 Years agowe need to find S= ∑tan(r)/[1+tan(r)] where r runs from 1 to 89
S= ∑1 – 1/[1+tan(r)]= ∑1 – ∑1/[1+tan(r)]= 89 – ∑1/[1+tan(r)]
now let P= ∑1/[1+tan(r)].....(1)
write P in reverse order, we get
P= ∑1/[1+tan(90 – r)]
P= ∑1/[1+cot(r)]
P= ∑tan(r)/[1+tan(r)].........(2)
add 1 and 2
2P= ∑[1+tan(r)]/[1+tan(r)]= ∑1= 89
or P= 89/2
so, S= 89 – P= 89 – 89/2
S= 89/2
kindly approve :)
Other Related Questions on trigonometry
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
In ABC, if cot A+cot B+cot C = cosecA cosecB cosecC, then prove that ABC is right angle triangle.
trigonometry
Last Activity: 3 Years ago
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
- Find the general solution of equation tan3∂=cot2∂
For all angles between -720 and +720
trigonometry
Last Activity: 4 Years ago
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
Derive a formula for the area of the triangle, given b, A, B, and C. That is, derive the formula: (b^2sinAsinC)/(2sinB)
trigonometry
Last Activity: 4 Years ago
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
WHAT IS THE LIMIT WHEN X TOWARDS TO 0 OF sin6x/5x ? lim𝑥→0 𝑠𝑖𝑛6𝑥/5𝑥
trigonometry
Last Activity: 4 Years ago