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phaansi ha order du kya ?
Sum of roots of sin^{-1}\frac{ax}{c}+sin^{-1}\frac{bx}{c}=sin^{-1}x is ?????
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26 Answers
1
62if
t is a solution here
then substitute x=-t
then the equality will also hold.. hence -t is also a root
21Ya sky!
Me too thot the same approach......
But Nishant Sir's 1-pt. Methid is 100times shortr than ours.........
and Its perfectly LOGICAL........ (widout ne kindof cheating [3] )
1so what do you want me to write
it was just an excalamation
like :
Heavens!!!
OMG !!!
.
.
and so on
1good lord !!
u solved it....[11]
but then u are not a minister for nothing........[1]
its ok i also got it now
1ax/c√1-b2x2/c2 + bx/c√1-a2x2/c2 = x
x[a/c√1-b2x2/c2 + b/c√1-a2x2/c2 - 1] =0
either x=0 or
[a/c√1-b2x2/c2 + b/c√1-a2x2/c2 - 1] =0
=> a2-c2-b2 = 2bc√1-a2x2/c2
so coeff of x here is 0.
=> sum of roots=0.
11there will certainly be more than two roots
but thing is they cancel each other for any number of even roots
1first of all someone convince me that there are only two roots
the rest would be easy then
11@ guys
i am pondering over this question 4 a long time
but my method is tedious and unending
if u have a better method then please do post a solution to this 1
11.) bang you for seeing the above post. [198]
2.) thanx for your solution. [51]
3.) i still cudn get. [3]
1Let x ε [-1.1] then -x ε [-1,1]
let sin-1(-x)=θ then -x=sinθ and θε[-Π/2,Π/2]
hence x= -sinθ = sin(-θ) and -θ ε [-Π/2,Π/2]
hence sin-1x = -θ = - sin-1(-x)
therefore sin-1(-x) = - sin-1 (x)
[1]
well, posted it since nishant bhaiya is not available... hope d lady emperor isn't angry wid me... :P
1if x is a root
then -x will also be a root
why??
i am being silly i think....
but i wud hide this one :P
allllllllllll telling great concept .. so GREAT CONCEPT BHAIYA!!
but... y ?
no one shud see,, other than nishant bhaiya.. [3] [51]
62arey yaar
if x is a root
then -x will also be a root
hence sum of roots is zero..
21yeh use kiya kya??
LHS = SIN-1(tx√1 - v2x2 + vx√1 - t2x2) = RHS = SIN-1x
11yes sir i also put x = ck
but i was a
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i was struck in the end[2][2][2]
62i think first simplification can be
a/c= t
b/c= v
but even that is not of too much use..
