Maths-
General
Easy

Question

sin space x plus sin space 2 x plus sin space 3 x equals cos space x plus cos space 2 x plus cos space 3 x if

  1. cos space x equals negative 1 half
  2. sin space 2 x equals cos space 2 x
  3. straight x equals fraction numerator straight n pi over denominator 2 end fraction plus pi over 8
  4. x equals 2 n pi plus-or-minus fraction numerator 2 pi over denominator 3 end fraction comma left parenthesis n element of I right parenthesis

The correct answer is: straight x equals fraction numerator straight n pi over denominator 2 end fraction plus pi over 8


    sin space x plus sin space 2 x plus sin space 3 x equals cos space x plus cos space 2 x plus cos space 3 x if
    sin space x plus sin space 2 x plus sin space open parentheses 2 x space plus space x close parentheses equals cos space x plus cos space 2 x plus cos space open parentheses 2 x space plus space x close parentheses
sin space x plus sin space 2 x plus sin space 2 x cos space x plus sin space x cos space 2 x equals cos space x plus cos space 2 x plus cos 2 x cos space x minus sin space x sin space 2 x
sin space x left curly bracket 1 plus cos space 2 x right curly bracket space plus sin space 2 x left curly bracket 1 plus cos space x right curly bracket equals cos space x left curly bracket space 1 plus cos space 2 x right curly bracket plus cos 2 x minus sin space x sin space 2 x
left parenthesis sin space x minus cos x minus 1 right parenthesis cos space 2 x space plus sin space 2 x left parenthesis 1 plus cos space x space plus sin x right parenthesis equals cos x space minus space sin space x

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