Prove that ("sin"^(-1)(2ab)/(a^(2)+b^(2)...

Prove that `("sin"^(-1)(2ab)/(a^(2)+b^(2))+"sin"^(-1)(2cd)/(c^(2)+d^(2)))` can be expressed in the form `"sin"^(-1)(2xy)/(x^(2)+y^(2))` where x and y are rational functions of a,b,c and d.

Verified by Experts

The correct Answer is:

`pi`

Similar Questions

Explore conceptually related problems

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

"If "y=sin^(-1)x, "find "(d^(2)y)/(dx^(2)) .

Prove that sin^2(A/2)+sin^2(B/2)-sin^2(C/2)=1-2cos(A/2)cos(B/2)sin(C/2)

If "sin"^(-1) (x)/(a)+"sin"^(-1)(y)/(b)="sin"^(-1)(c^(2))/(ab) , prove that, b^(2)x^(2)+2xy sqrt(a^(2)b^(2)-c^(4))+a^(2)y^(2)=c^(4)

sin ^(-1)""(ax)/(C ) +sin ^(-1) ""(bx)/(c ) =sin ^(-1)""x where a^(2)+b^(2)=c^(2) and c ne 0

(x) (a sin(B-C))/(b^(2)-c^(2)) = (b sin (C-A))/(c^(2)-a^(2)) = (c sin(A-B))/(a^(2)-b^(2))

sin^(-1)x+sin^(-1)y=cos^(-1)""{sqrt((1-x^(2))(1-y^(2)))-xy}

Prove : int (sin^(8) x - cos ^(8)x)/(1-2sin^(2) x cos ^(2) x) dx = - 1/2 sin 2x + c

A+B+C=pi ,prove that sin^2(A/2)+sin^2(B/2)+sin^2(C/2)=1-2sin(A/2)sin(B/2)sin(C/2)

In triangle ABC, if a^(2) + b^(2) +c^(2) -bc -ca -ab=0, then the value of sin ^(2)A+ sin ^(2)B+sin ^(2)C is -