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

+4 votes
1/(csc x+1)
asked Jan 25, 2013 in TRIGONOMETRY by anonymous Apprentice

2 Answers

+3 votes

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)

answered Jan 25, 2013 by richardson Scholar
+4 votes

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)

 

answered Jan 25, 2013 by Naren Answers Apprentice

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