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Trignometry

New kid on the Block

 Joined: 7 May 2012 Post: 7
7 May 2012 23:39:38 IST
0 People liked this
2
306
heights and distances
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Trigonometry

A ladder rest against a wall at an angle 'X' to the horizontal.Its foot is pulled away from the wall through a distance 'a' so that it slides a distance 'b' down wall making an angle 'Y' with the horizontal then tan(X+Y) is equal to...???Plz explain the steps to solve dis prob.

Ans:  (2ab) / (a^2-b^2)

Plz explain the steps to solve dis prob.

Blazing goIITian

Joined: 22 May 2009
Posts: 2467
8 May 2012 15:55:00 IST
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take initial height as p and distance of lader foot from wall be q and its length be L

now sinx=p\L...1

cosx=q\L..2

now on taking the second condition height would be p-b and distance would be q+a

so

siny=(p-b)\L....3

cosy=(q+a)/L...4

using 1 and 3 (just subtract)
2sin(x-y)/2cos(x+y)/2=b\L

using 2 and 4(just subtract)

2sin(x-y)/2sin(x+y)/2=a\L

divide the above two expression

tan(x+y)/2=a/b

apply tan2@ formulae u will get tan(x+y)...

New kid on the Block

Joined: 7 May 2012
Posts: 7
8 May 2012 17:12:03 IST
0 people liked this

thnx

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