cos2A+cos2B+cos2C=-1-4cosAcosBcosC.

Asked by sangitapatel93901 | 18th Jun, 2019, 07:50: PM

Expert Answer:

I n space t r i a n g l e space A B C comma space A plus B plus C equals 180 degree equals straight pi
C o n s i d e r comma
cos 2 A plus cos 2 B plus cos 2 C
equals 2 cos left parenthesis A plus B right parenthesis space cos left parenthesis A minus B right parenthesis plus left parenthesis 2 cos squared C minus 1 right parenthesis
equals 2 cos left parenthesis straight pi minus straight C right parenthesis cos left parenthesis straight A minus straight B right parenthesis plus 2 cos squared straight C minus 1
equals negative 2 cosCcos left parenthesis straight A minus straight B right parenthesis plus 2 cos squared straight C minus 1
equals negative 1 minus 2 cosC open square brackets cos left parenthesis straight A minus straight B right parenthesis minus cosC close square brackets
equals negative 1 minus 2 cosC open square brackets cos left parenthesis straight A minus straight B right parenthesis minus cos left parenthesis straight pi minus left parenthesis straight A plus straight B right parenthesis right parenthesis close square brackets
equals negative 1 minus 2 cosC open square brackets cos left parenthesis straight A minus straight B right parenthesis plus cos left parenthesis straight A plus straight B right parenthesis close square brackets
equals negative 1 minus 2 cosC open square brackets 2 cosA space cosB close square brackets
equals negative 1 minus 4 cosA space cosB space cosC
Hence comma space cos 2 straight A plus cos 2 straight B plus cos 2 straight C equals negative 1 minus 4 cosA space cosB space cosC.

Answered by Renu Varma | 19th Jun, 2019, 02:09: PM

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