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if tan -1 [ { (1+x 2 ) 1/2 – (1-x 2 ) 1/2 } / {(1+x 2 ) 1/2 + (1-x 2 ) 1/2 } ] = t, then ptove that x 2 = sint

if tan-1[ { (1+x2)1/2 – (1-x2)1/2  } / {(1+x2)1/2 + (1-x2)1/2 } ] = t,
then ptove that x2 = sint

Grade:12

1 Answers

Arun
25757 Points
5 years ago
 

let tan-1{(1+x2)1/2- (1-x2)1/2}/(1+x2)1/2+(1-x2)1/2  = t

then

[{(1+x2)1/2 - (1-x2)1/2} / {((1+x2)1/2 + (1-x2)1/2) = tan t

Now apply C and D to get,

{1-x2/1+x2}1/2  =  1-tant/1+tant

expand RHS by writing tan t = sint/cost.

squaring,

{1-x2/1+x2}  = {cost - sint/cost + sint}2

{1-x2/1+x2} = 1- sin2t/1+sin2t

so x2 =sint 

 

 

Regards

Arum (askIITians forum.expert)

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