Rewrite the expression so that it is not in fractional form:

Question

1/(csc x+1)

Answer 1

1 /( cscx+1)

Consider

cscx + 1

Recall: cscx = 1/ sinx

(1/sinx) + 1

Here LCM of sinx, 1 is sinx

(1 + sinx) / sinx

1 /( cscx+1) = 1 / [(1 + sinx) / sinx]

= 1 / [(1 + sinx) / sinx]

Note : 1 /(a/b) = b/a

= sinx / (1 + sinx)

Answer 2

1 /( cscx+1)

First simplify the denominator = cscx + 1

Recall inverse trigonometric identities: cscx = 1/ sinx

= (1/sinx) + 1

= (1 + sinx) / sinx

 

Substitute the derived expression in original expression

1 /( cscx+1) = 1 / [(1 + sinx) / sinx]

= sinx / (1 + sinx)