If sin-1 x + sin-1 y = π/2, then x2 is equal to 1) y2 2)(1-y)1/2 3) 1 – y2 4) 0

Dear Tushar , We Know thatSin-1x + cos-1x = /2And Given is that Sin-1x + Sin-1y = /2 Therefore , we get that...Sin-1y = cos-1xSin-1y = Sin-1() Thereforey = On Squaring both sides .we get x2 = 1 – y2

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Trigonometry> If sin -1 x + sin -1 y = π/2 , then ...

If sin^-1 x + sin^-1 y = π/2,
then x² is equal to 1) y² 2)(1-y)^1/2 3) 1 – y² 4) 0

Tushar Kasturi , 8 Years ago

Grade 12

2 Answers

Shahid

Last Activity: 8 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

x² = 1 – y²

ankit singh

Last Activity: 5 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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Trigonometry> If sin ​-1 x + sin ​ ​-1 y = π/2 , then ​...

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

Tushar Kasturi , 8 Years ago

Shahid

ankit singh

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