Solve the equation: `cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)(1/a)`

Solve the equation: `cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1

1.	Solve the equation: `cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)(1/a)`
Answer» `cos^-1 (a/x) + cos^-1 (1/a) = cos^-1(b/x) + cos^-1 (1/b) ` `cos^-1 x + cos^-1 y = cos^-1 (xy - sqrt(1-x^2) sqrt(1-y^2))` `cos^-1 (a/x 1/a - sqrt(1- a^2/x^2)sqrt(1- 1/a^2))` `cos^-1 (b/x*1/b - sqrt(1- b^2/x^2) sqrt(1- 1/b^2))` `(1- a^2/x^2) (1-1/a^2) = (1- b^2/x^2)(1- 1/b^2) ` `= 1- 1/a^2 - a^2/x^2 + 1/x^2 = 1- 1/b^2 - b^2/x^2 + 1/x^2` `a^2/x^2 - b^2/x^2 = 1/b^2 - 1/a^2` `= 1/x^2 [ a^2- b^2] = (a^2- b^2)/(a^2b^2) ` `x^2 = (ab)^2` `x= ab` Answer

Prove that:`sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)=pi`
What is greater, `tan1 or tan^(-1)1?`
In a ` A B C ,`, if C is a right angle, then `tan^(-1)(a/(b+c))+tan^(-1)(b/(c+a))=``pi/3`(b) `pi/4`(c) `(5pi)/2`(d) `pi/6`
Prove that:`(i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-cosx))}=pi/4+x/2`,
Prove that `tan(cot^(-1)x)=cot(tan^(-1)x)`
Write the value of `sin^-1(sin1550^@)`
Prove that:`tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2`
Write the value of `cos^2(1/2cos^(-1)3/5)`
Solve the equation: `cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)(1/a)`
If `tan^(-1)x+tan^(-1)y=pi/4,`then write the value of `x+y+x ydot`