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#