Verified answer

Since cot 240 = 1 / tan 240,

cot 240 x tan 240 = 1.

Hence,

given expression = 1 / sin 240 = csc 240.

........................................................................................

FYI

..................

sin 240 = sin ( 180 + 60 ) = sin 60 = ( sqrt 3 ) / 2

so that

csc 240 = 1 / sin 240 = 1 / ( sqrt 3)/2 = 2 / ( sqrt 3 ).

........................................................................................

Happy To Help !

csc 240º = 1/sin 240º

cot 240º = 1/tan 240º

So,

(cot 240° tan 240°)/(sin 240°) = csc 240°

((1/tan 240º) * tan 240º)/sin(240º) = 1/sin 240º

1/sin 240º = 1/sin 240º

QED

cot and tan are reciprocals so the numerator =1:

1/sin240 =csc240