If `sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x ,` then `x` is equal to `[a , b , in (0,1)]` (a)`(a-b)/(1+a b)` (b) `b/(1+a b)` (c) `b/(1+a b)` (d) `(a+b)/(1-a b)`

sin ^(-1) ""(2a)/(1+a^(2))+sin ^(-1) ""(2b)/(1+b^(2) ) = 2 tan ^(-1) x

sin^(-1) ""(2a)/(1+a^(2))-cos^(-1) ""(1-b^(2))/(1+b^(2))=2tan ^(-1) ""(a-b)/(1+ab)

If (1)/(a)+(1)/(c )=(1)/(2b-a)+(1)/(2b-c) , then

If sin^(-1)(a-a^2/3+a^3/9-...)+cos^(-1)(1+b+b^2+...)=pi/2 then find a and b

If af(x+1)+bf(1/(x+1))=x ,x!=-1,a!=b ,t h e nf(2) is equal to (a) (2a)/(2(a^2-b^2)) (b) a/(a^2-b^2) (c) (a+2b)/(a^2-b^2) (d) none of these

If (log)_4 5=aa n d(log)_5 6=b , then (log)_3 2 is equal to 1/(2a+1) (b) 1/(2b+1) (c) 2a b+1 (d) 1/(2a b-1)

Solve: (a+x-2b)/(2a-b)-(a-2b)/x=1 .

If sin^(-1)a+sin^(-1)b+sin^(-1)c=pi, then the value of asqrt((1-a^2))+bsqrt((1-b^2))+csqrt((1-c^2)) will be (A) 2a b c (B) a b c (C) 1/2a b c (D) 1/3a b c

The asymptotes of the hyperbola (x^(2))/(a_(1)^(2))-(y^(2))/(b_(1)^(2))=1 and (x^(2))/(a_(2)^(2))-(y^(2))/(b_(2)^(2))=1 are perpendicular to each other. Then, (a) a_(1)/a_(2)=b_(1)/b_(2) (b) a_(1)a_(2)=b_(1)b_(2) (c) a_(1)a_(2)+b_(1)b_(2)=0 (d) a_(1)-a_(2)=b_(1)-b_(2)

If a^(2)/(b + c) = b^(2)/(c +a) = c^(2)/(a + b) = 1 , then show that 1/(1+a) + 1/(1 + b) + 1/(1+c) = 1 .