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EXPERTS DONT SAY POST THIS QUERY IN ASKTHE EXPERT SECTION. IAM UNABLE TO SOLVE THIS SO PLZZ SOLVE IT IN SIMPLE WAY.
 
PROVE THAT-
 
cos2x cosx/2 - cos3x cos 9x/2 = sin5x sin 5x/2

Asked by nikitaayyagari 25th February 2016, 6:17 PM
Answered by Expert
Answer:

begin mathsize 12px style Hi space Nikita comma For space some space questions comma space we space ask space you space to space post space the space query space in space ask space the space expert space section comma space as space it space is space not space possible space to space give space detailed space solution space to space straight a space lengthy space question space during space the space chat space session space due space to space time space constraint. However comma space in space such space scenario comma space we space try space our space best space to space give space you space some space hint space on space how space to space solve space the space question. space The space solution space to space your space query space is space as space follows colon LHS equals cos 2 xcos straight x over 2 minus cos 3 xcos fraction numerator 9 straight x over denominator 2 end fraction equals fraction numerator cos open parentheses 2 straight x minus begin display style straight x over 2 end style close parentheses plus cos open parentheses 2 straight x plus begin display style straight x over 2 end style close parentheses over denominator 2 end fraction minus fraction numerator cos open parentheses 3 straight x minus begin display style fraction numerator 9 straight x over denominator 2 end fraction end style close parentheses plus cos open parentheses 3 straight x plus begin display style fraction numerator 9 straight x over denominator 2 end fraction end style close parentheses over denominator 2 end fraction equals fraction numerator cos begin display style fraction numerator 3 straight x over denominator 2 end fraction end style plus cos begin display style fraction numerator 5 straight x over denominator 2 end fraction end style over denominator 2 end fraction minus fraction numerator cos open parentheses negative begin display style fraction numerator 3 straight x over denominator 2 end fraction end style close parentheses plus cos begin display style fraction numerator 15 straight x over denominator 2 end fraction end style over denominator 2 end fraction equals fraction numerator cos begin display style fraction numerator 5 straight x over denominator 2 end fraction end style minus cos begin display style fraction numerator 15 straight x over denominator 2 end fraction end style over denominator 2 end fraction equals fraction numerator negative 2 sin open parentheses begin display style fraction numerator begin display style fraction numerator 5 straight x over denominator 2 end fraction end style plus begin display style fraction numerator 15 straight x over denominator 2 end fraction end style over denominator 2 end fraction end style close parentheses sin open parentheses begin display style fraction numerator begin display style fraction numerator 5 straight x over denominator 2 end fraction end style minus begin display style fraction numerator 15 straight x over denominator 2 end fraction end style over denominator 2 end fraction end style close parentheses over denominator 2 end fraction equals fraction numerator negative 2 sin 5 xsin open parentheses negative begin display style fraction numerator 10 straight x over denominator 4 end fraction end style close parentheses over denominator 2 end fraction equals fraction numerator 2 sin 5 xsin begin display style fraction numerator 5 straight x over denominator 2 end fraction end style over denominator 2 end fraction equals sin 5 xsin fraction numerator 5 straight x over denominator 2 end fraction equals RHS space left parenthesis Proved right parenthesis end style

Answered by Expert 25th February 2016, 6:49 PM
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