Maths-
General
Easy

Question

if square root of fraction numerator 1 minus sin space A over denominator 1 plus sin space A end fraction end root equalssec A-tan A then  lies in the quadrants

  1. I, II  

  2. II, III   
  3. I, IV
  4. I, III

hintHint:

We know that,
sin space x space greater or equal than 0   in the first and second quadrant.
cos space x space greater or equal than 0   in the first and fourth quadrant.
tan space x space greater or equal than 0   in the first and third quadrant.

The correct answer is: I, IV


    Step by step solution:
    square root of fraction numerator 1 minus sin space A over denominator 1 plus sin space A end fraction end root equalssquare root of fraction numerator open parentheses 1 minus sin A close parentheses squared over denominator open parentheses 1 plus sin A close parentheses open parentheses 1 minus sin A close parentheses end fraction end root  [rationalizing]
    equals square root of fraction numerator left parenthesis 1 minus sin A right parenthesis squared over denominator 1 minus sin squared A end fraction end rootequals square root of open parentheses fraction numerator 1 minus sin A over denominator cos A end fraction close parentheses squared end rootequals square root of open parentheses s e c A minus tan A close parentheses squared end root
    equals open vertical bar s e c A minus tan A close vertical bar
    Now, given in the question that open vertical bar s e c A minus tan A close vertical barequals s e c A minus tan A
    We know that open vertical bar x close vertical bar equals x only for x greater or equal than 0
    Therefore, s e c A minus tan A greater or equal than 0
    rightwards double arrow s e c A greater or equal than tan A
    rightwards double arrow cos A greater than 0
    Thus, A lies in first and fourth quadrant.
    Hence, option(c) is the correct option.

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