How to simplify #sin(sec^(-1)(x))# ?

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Answer 1 · 2018-08-02T23:13:23

#sin(sec^(-1)(x))=sqrt(x^2-1)/x#

#sin(sec^(-1)(x))=sin(cos^(-1)(1/x))#

Let #y=cos^(-1)(1/x)#

#x=1/cos(y)#

#1/x^2=cos(y)^2=1-sin(y)^2#

#1/x^2-1=-sin(y)^2#

#(x^2-1)/x^2=sin(y)^2#

#sqrt(x^2-1)/x=sin(y)=sin(sec^(-1)(x))#

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