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Show That: 2sin^-1(3/5)=tan^-1(24/7) - Mathematics and Statistics

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Show that: `2sin^-1(3/5)=tan^-1(24/7)`

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Solution

`Let x=sin^(-1)(3/5)`

`sinx=3/5`

`tan x=(3/4)`

x=

`x=tan^(-1)(3/4)`

`sin^(-1)(3/5)=tan^(-1)(3/4)`

`2sin^(-1)(3/5)=2tan^(-1)(3/4)`

`=tan^(-1)(3/4)+tan^(-1)(3/4)`

`=tan^(-1)(((3/4)+(3/4))/(1-3/4(3/4)))`

`=tan^(-1)((6/4)/(7/16))`

`=tan^(-1)(6/4 xx 16/7)`

`=tan^(-1)(24/7)`

`sin^(-1)(3/5)=tan^(-1)(24/7)`

Concept: Basic Concepts of Trigonometric Functions
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