" Q.60"quad " If "quad y=sqrt((1-x)(1+x))" ,then "

If sin (x + y) = p/sqrt(1 + p^(2)) " and " cos (x - y) = 1/sqrt(1 + q^(2)) "then show that " tan x " is a root of the equation " (p + q)z^(2) + 2(1 - pq) z- (p + q) = 0

If e^(y)=(sqrt(1+x)+sqrt(1-x))/(sqrt(1+x)-sqrt(1-x))," then "(dy)/(dx)=

If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y) , then prove that (dy)/(dx)= sqrt((1-y^(2))/(1-x^(2))) . (Where |x| le 1, |y| le 1 )

If y=sqrt(x)+(1)/(sqrt(x)) , then (dy)/(dx) at x=1 is

y=(sqrt(x)+(1)/(sqrt(x)))(1+x+x^(2))

If y=log(sqrt(x)+(1)/(sqrt(x)))^(2), then , x(x+1)^(2)y_(2)+(x+1)^(2)y_(1) is

Prove that sin ^ (- 1) x + cos ^ (- 1) y = (tan ^ (- 1) (xy + sqrt ((1-x ^ (2)) (1-y ^ (2)))) ) / (y sqrt (1-x ^ (2)) - x sqrt (1-y ^ (2)))