Answer to Question #183804 in Trigonometry for Rebira

Question

cos^-1(sin^-1(tan^-1(x)))

Answer 1

Let y=cos^-1(sin^-1(tan^-1(x))).

$y=cos^{-1}(sin^{-1}(tan^{-1}(x)))\newline \text{Taking cosine both side,}\newline cos(y)=sin^{-1}(tan^{-1}(x))\newline \text{Taking sine both side,}\newline sin(cos(y))=tan^{-1}(x)\newline \text{Taking tangent both side,}\newline tan(sin(cos(y)))=x$

Thus, for any value of y there exist x i.e., x=tan(sin(cos(y))).