Home
Class 12
MATHS
If y = sin^(-1) ( x sqrt(1-x) + sqrtx s...

If ` y = sin^(-1) ( x sqrt(1-x) + sqrtx sqrt( 1- x^2) ) and (dy)/(dx) = 1/(2 sqrt(x(1-x)) )+ p`, then p,

Text Solution

Verified by Experts

`y = sin^-1(xsqrt(1-x)+sqrtxsqrt(1-x^2))->(1)`
Let `x = sin theta`
Then, `cos theta = sqrt(1-x^2)`
Let `sqrt x = sin phi`
then, `cos phi = sqrt(1-x)`
Putting these values in (1),
`=>y = sin^-1(sinthetacosphi + costheta sinphi)`
`=>y = sin^-1(sin(theta+phi)`
...
Promotional Banner

Similar Questions

Explore conceptually related problems

If y = sin^(-1) (x sqrt(1-x) - sqrtx sqrt(1-x^(2))) then dy/dx =

If y=sin ^(-1) (xsqrt( 1-x) +sqrt(x) sqrt (1-x^(2))),then (dy)/(dx)=

If y = sin^-1[xsqrt(1-x) - sqrtx (sqrt(1-x^2))] find dy/dx

If y=sin^(-1)(xsqrt(1-x)+sqrt(x)sqrt(1-x^2)) and (dy)/(dx)=1/(2sqrt(x(1-x)))+p , then p is equal to 0 (b) 1/(sqrt(1-x)) sin^(-1)sqrt(x) (d) 1/(sqrt(1-x^2))

If y=sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^(2))] then find (dy)/(dx)

y = sin^(-1) {(sqrt(1 +x) + sqrt(1 -x))/(2)} " then " (dy)/(dx) = ?

If y=sin^(-1)[x sqrt(1-x)-sqrt(x)sqrt(1-x^(2))) and 0