Question

Pleaaaaseee help !!!!!

Answer 1

let assume

$sin( {tan}^{ - 1} 5) = sin \: y \\ so \: y \: = {tan}^{ - 1} 5 \: \\ tan \: y \: = 5$

we know from defination of inverse function

tan y = opposite / adjacent

here opposite is 5 and adjacent is 1

tan y = 5/1

lets calculate hypotenus using pythagoras theorem

hypotenuse = root ( 5^2 + 1^2)= root (25+1) = root (26)

now we know

sin y = opposite / hypotenus

so

$sin \: y \: = \frac{5}{ \sqrt{26} } \\ sin \: ( {tan}^{ - 1} x)\: = \frac{5}{ \sqrt{26} }$

hope it helps you