Home
Class 12
MATHS
If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2...

If `sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x` then `x=`

A

`(a - b)/(1 + ab)`

B

`(b)/(1 + ab)`

C

`(b)/(1 - ab)`

D

`(a + b)/(1 - ab)`

Text Solution

Verified by Experts

Since `sin^(-1) ((2x)/(1 + x^(2))) = 2 tan^(-1) x " for " x in (-1, 1)`
`sin^(-1) ((2a)/(1 + a^(2))) + sin^(-1) ((2b)/(1 + b^(2))) = 2 tan^(-1) x`
`rArr 2 tan^(-1) a + 2 tan^(-1) b = 2 tan^(-1) x`
or `tan^(-1) a + 2 tan^(-1) b = 2 tan^(-1) x`
or `tan^(-1) ((a + b)/(1 -ab)) = tan^(-1) x`
or `x = (a + b)/(1 - ab)`
Promotional Banner

Similar Questions

Explore conceptually related problems

If sin^(-1) ((2a)/(1 +a^(2))) + sin^(-1) ((2b)/(1 + b^(2))) = 2tan^(-1) x , then x is equal to

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

If sin^(-1)((2a)/(1+a^(2)))+sin^(-1)((2b)/(1+b^(2)))=2tan^(-1)x , then, x = ____

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)

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)

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)

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)

If Sin^(-1)((2a)/(1+a^(2)))+Sin^(-1)((2b)/(1+b^(2)))=2Tan^(-1)x , then x =

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