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if tan inverse[{(1+x 2 ) 1/2 - (1-x 2 ) 1/2 } / {((1+x 2 ) 1/2 + (1-x 2 ) 1/2 )} = a then x 2 =________ ans: sin2a

if tan inverse[{(1+x2)1/2 - (1-x2)1/2} / {((1+x2)1/2 + (1-x2)1/2)} = a then x2=________


 


ans: sin2a

Grade:12

1 Answers

Priyansh Goel
21 Points
14 years ago

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

then

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

Now apply C and D to get,

{1-x2/1+x2}1/2  =  1-tana/1+tana

expand RHS by writing tan a = sina/cosa.

squaring,

{1-x2/1+x2}  = {cosa - sina/cosa + sina}2

{1-x2/1+x2} = 1- sin2a/1+sin2a

so x2 =sin2a.

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