Maths-
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Easy

Question

In straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan invisible function application A over 2 plus tan invisible function application B over 2 close parentheses tan invisible function application C over 2 equals

  1. c
  2. c over 2
  3. 2 straight c
  4. 3 straight c

hintHint:

To solve the given question when it is given ABC is a triangle, firstly we can write a+b+c= 2s then we will use the formula tan space A over 2 equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis end fraction end root space comma space tan space B over 2 equals square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root space a n d space tan space C over 2 equals square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus a right parenthesis over denominator s left parenthesis s minus c right parenthesis end fraction end root.

The correct answers are: c over 2, 2 straight c


    In straight triangle A B C comma left parenthesis a plus b plus c right parenthesis open parentheses tan invisible function application A over 2 plus tan invisible function application B over 2 close parentheses tan invisible function application C over 2 equals
    2 s left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis left parenthesis s minus c right parenthesis over denominator s left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus c right parenthesis left parenthesis s minus a right parenthesis over denominator s left parenthesis s minus b right parenthesis end fraction end root space right parenthesis left parenthesis square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator s left parenthesis s minus c right parenthesis end fraction end root right parenthesis space space space space space space space space space space space space space space space space space space space space space space space left parenthesis a plus b plus c equals 2 s right parenthesis
equals 2 s cross times square root of fraction numerator left parenthesis s minus c right parenthesis over denominator s squared end fraction space end root space left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis over denominator left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis end fraction end root right parenthesis left parenthesis square root of fraction numerator left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis over denominator left parenthesis s minus c right parenthesis end fraction end root right parenthesis
equals 2 square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root space left parenthesis square root of fraction numerator left parenthesis s minus b right parenthesis over denominator left parenthesis s minus a right parenthesis end fraction end root plus square root of fraction numerator left parenthesis s minus a right parenthesis over denominator left parenthesis s minus b right parenthesis end fraction end root right parenthesis
equals 2 square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root fraction numerator square root of s minus b end root cross times square root of s minus b end root plus square root of s minus a end root cross times square root of s minus a end root over denominator square root of left parenthesis s minus a right parenthesis left parenthesis s minus b right parenthesis end root end fraction
equals 2 left parenthesis s minus b plus s minus a right parenthesis
equals 2 left parenthesis 2 s minus left parenthesis a plus b right parenthesis right parenthesis
equals 2 left parenthesis 2 s minus 2 s plus c right parenthesis
equals 2 c

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