What is $tan(arcsin (5/13))$ ?

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Answer 1 · 2018-07-11T04:56:36

$tan(arc sin(5/13))=5/12$

We know that ,

$color(red)((1)arc sin(x)=arc tan(x/sqrt(1-x^2)) , x in ( 0 ,1)$

$color(blue)((2)tan(arc tan(x))=x ,AA x in RR$

Let ,

$y=tan(arc sin(5/13))...tocolor(red)(Apply(1)$

$=>y=tan(arctan((5/13)/sqrt(1-(5/13)^2)))$

$=>y=tan(arctan(5/sqrt(13^2-5^2)))$

$=>y=tan(arc tan(5/12))...tocolor(blue)(Apply(2)$

$=>y=5/12$

What is tan(arcsin (5/13))tan(arcsin (5/13))?