If sin^-1(x) +sin^-1(y)=pi/2, then what will dy/dx be?
2 Answers
Jan 30, 2018
Let's have a look.
Explanation:
This problem involves both differentiation as well as inverse trigonometric functions.
Now given that,
hope it Helps :)
Jan 30, 2018
dy/dx = - sqrt(1-y^2)/sqrt(1-x^2)
Explanation:
We have:
sin^(-1)x + sin^(-1)y = pi/2
Using the standard result:
d/dx sin^(-1) x = 1/sqrt(1-x^2)
we can implicitly differentiate the first equation, giving:
1/sqrt(1-x^2) + 1/sqrt(1-y^2) dy/dx = 0
:. 1/sqrt(1-y^2) dy/dx = - 1/sqrt(1-x^2)
:. dy/dx = - sqrt(1-y^2)/sqrt(1-x^2)