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If sin ​-1 x + sin ​ ​-1 y = π/2 , then ​ x ​2 is equal to 1) y ​2 2)(1-y) ​1/2 3) 1 – y ​2 4) 0

  If sin​-1 x + sin​​-1 y = π/2,
  then ​x​2 is equal to                                                      1) y​2                  2)(1-y)​1/2            3) 1 – y​2     4) 0

Grade:12

2 Answers

Shahid
74 Points
6 years ago
Dear Tushar , 
We Know that
Sin-1x + cos-1x = \Pi/2
And Given is that Sin-1x + Sin-1y = \Pi/2
 
Therefore , we get that...
Sin-1y = cos-1x
Sin-1y = Sin-1(\sqrt{1 - x^{2}}) 
 
Therefore
y = \sqrt{1 - x^{2}}
 
On Squaring both sides .
we get
 
x​2  = 1 – y​2
ankit singh
askIITians Faculty 614 Points
2 years ago
his problem involves both differentiation as well as inverse trigonometric functions.

Now given that,

sin−1x+sin−1y=π2

∴sin−1x=π2−sin−1y

∴sin−1x=cos−1y

∴y=cossin−1x

∴dydx=−sinsin−1x.ddx(sin−1x)

∴dydx=−x1√1−x2

∴dydx=−x√1−x2.

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