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 \: = (5)/( √(26) ) \\ sin \: ( {tan}^( - 1) x)\: = (5)/( √(26) )`

hope it helps you