If sin^-1(x) +sin^-1(y)=pi/2, then what will dy/dx be?

2 Answers

Let's have a look.

Explanation:

This problem involves both differentiation as well as inverse trigonometric functions.

Now given that,

sin^(-1)x+sin^(-1)y=pi/2

:.sin^(-1)x=pi/2-sin^(-1)y

:.sin^(-1)x=cos^(-1)y

:.y=cossin^(-1)x

:.dy/dx=-sinsin^(-1)x.d/dx(sin^(-1)x)

:.dy/dx=-x1/sqrt(1-x^2)

:.color(red)(dy/dx=-x/sqrt(1-x^2)).

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)