Maths-
General
Easy

Question

In straight triangle A B C comma left parenthesis a minus b right parenthesis squared cos squared invisible function application c over 2 plus left parenthesis a plus b right parenthesis squared sin squared invisible function application c over 2 equals

  1. c
  2. c over 2
  3. 2 c
  4. c squared

Hint:

To find the value of the given equation we will use the cosine formula of a triangle.

The correct answer is: c squared


    In straight triangle A B C comma left parenthesis a minus b right parenthesis squared cos squared invisible function application c over 2 plus left parenthesis a plus b right parenthesis squared sin squared invisible function application c over 2 equals
    left parenthesis a squared plus b squared minus 2 a b right parenthesis space cos squared C over 2 plus left parenthesis a squared plus b squared plus 2 a b right parenthesis sin squared C over 2
equals a squared cos squared C over 2 plus b squared cos squared C over 2 minus 2 a b cos squared C over 2 plus a squared sin squared C over 2 plus b squared sin squared C over 2 plus 2 a b sin squared C over 2
equals a squared left parenthesis cos squared C over 2 plus sin squared C over 2 right parenthesis plus b squared left parenthesis cos squared C over 2 plus sin squared C over 2 right parenthesis minus 2 a b left parenthesis cos squared C over 2 minus sin squared C over 2 right parenthesis
equals a squared plus b squared minus 2 a b space cos C space space space space space space left parenthesis b y comma cos squared x plus sin squared x equals 1 right parenthesis comma left parenthesis b y comma cos squared x minus sin squared x equals cos 2 x right parenthesis
equals c squared space space space space space space space space space space space space space space space space space space space space left parenthesis b y space cos i n e space f o r m u l a comma space c squared equals a squared plus b squared minus 2 a b space cos C right parenthesis

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