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

Question

35255 views around the world

You can reuse this answer
Creative Commons License

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 $y=cos^(-1)(1/x)$

$x=1/cos(y)$

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

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

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

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

\0/ here's our answer !

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