Maths-
General
Easy

Question

If the point left parenthesis 1 plus cos invisible function application theta comma sin invisible function application theta right parenthesis lies between the region corresponding to the acute angle between the lines x-3y=0 and x-6y=0 then

  1. theta element of straight R
  2. theta element of straight R minus straight n pi comma straight n element of straight I
  3. theta element of straight R minus open parentheses straight n pi plus pi over 2 close parentheses comma straight n element of straight I
  4. None of these

hintHint:

If a point lies inside an acute angle of two lines. Then, the product of their values should be less than zero.

The correct answer is: None of these


    Given That:
    If the point left parenthesis 1 plus cos invisible function application theta comma sin invisible function application theta right parenthesis lies between the region corresponding to the acute angle between the lines x-3y=0 and x-6y=0 then
    >>> We know that when the point lies in between the lines then product of their values should be less than 0.
    >>> L11cross timesL22 <0.
    >>> L11 becomes (1+costheta)-3(sintheta)
    >>> L22 becomes (1+costheta)-6(sintheta)
    >>> Therefore:
    L11 cross times L22 <0
    ( (1+costheta)-3(sintheta))cross times((1+costheta)-6(sintheta))<0
    (1+costheta)2 -6sintheta -6sinthetacostheta -3sintheta-3sinthetacostheta+18sintheta2 < 0
    >>> Therefore, evaluate for theta.

    >>> L11 cross times L22 <0
    >>>   (1+costheta)2 -6sintheta -6sinthetacostheta -3sintheta-3sinthetacostheta+18sintheta2 < 0

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