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2Tan^(-1)(3//4)=...

`2Tan^(-1)(3//4)=`

A

`Sin^(-1)(24//25)`

B

`Sin^(-1)(12//13)`

C

`Sin^(-1)(23//24)`

D

`Sin^(-1)(13//12)`

Text Solution

Verified by Experts

The correct Answer is:
A
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sin(2"Tan"^(-1)3/4)=

Find the values of the following: sin^(2)("Tan"^(-1)3/4)

The ascending order of A=cos("sin"^(-1)12/13), B=sin(2"Tan"^(-1)3/4), C=tan(1/2"Cos"^(-1)1/3) is

1/3gt0,3/4gt0impliestan^(-1)(1/3)-tan^(-1)(3/4) =tan^(-1)((1/3-3/4)/(1+1/3 . 3/4))=tan^(-1)((-5)/15)=tan^(-1)(1/3) =-tan^(-1)(1/3)

5/3gt0,1/4gt0impliestan^(-1)(5/3)-tan^(-1)(1//4) =tan^(-1)((5/3-1/4)/(1+5/3. 1/4))=tan^(-1)(1)=(pi)/4

tan^(-1)(2+)tan^(-1)(3)=

tan("Tan"^(-1)1/2+"Tan"^(-1)1/3)=

tan^(-1)(1/2)+tan^(-1)(1/3)=