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    Maths-
    General
    Easy

    Question

    The sides of a triangle aresin invisible function application alpha comma cos invisible function application alpha text  and  end text square root of 1 plus sin invisible function application alpha cos invisible function application alpha end root text  for some  end text 0 less than alpha less than pi over 2 Then the greatest angle of the triangle is  [AIEEE 2014]

    1. 60 to the power of ring operator
    2. 150 to the power of ring operator
    3. 120 to the power of ring operator
    4. 90 to the power of ring operator

    hintHint:

    In this question, we have to find sin invisible function application alpha comma cos invisible function application alpha text  and  end text square root of 1 plus sin invisible function application alpha cos invisible function application alpha end root text  for some  end text 0 less than alpha less than pi over 2. As c is the largest side so C is the greatest angle, so, by using cosine formula we can find the largest angle of the triangle.

    The correct answer is: 120 to the power of ring operator

      L e t space a equals sin space alpha comma b equals cos space alpha space a n d space c equals square root of 1 plus sin space alpha cos space alpha end root space comma space 0 less than alpha less than pi over 2 A s space c space i s space t h e space l a r g e s t space s i d e comma space s o space angle C space i s space t h e space g r e a t e s t space a n g l e. space cos space C space equals fraction numerator a squared plus b squared minus c squared over denominator 2 a b end fraction space space space space space space space space space space space equals fraction numerator sin squared space alpha plus cos squared space alpha space minus open parentheses square root of 1 plus sin space alpha space cos space alpha end root close parentheses squared space over denominator 2 space sin space alpha space cos space alpha end fraction space space space space space space space space space space space equals fraction numerator sin squared space alpha space plus cos squared space alpha space minus 1 minus sin space alpha. cos space alpha over denominator 2 space sin alpha space cos alpha end fraction space space space space space space space space space space space equals fraction numerator 1 minus 1 minus sin space alpha. cos space alpha over denominator 2 sin space alpha. cos space alpha end fraction space space space space space space space space space space equals fraction numerator negative sin space alpha. cos space alpha over denominator 2 sin space alpha. cos space alpha end fraction space space space space space space space space space equals fraction numerator negative 1 over denominator 2 end fraction rightwards double arrow cos space C space equals fraction numerator negative 1 over denominator 2 end fraction rightwards double arrow cos space C equals cos space 120 degree rightwards double arrow C equals 120 degree

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