I f space A plus B plus C equals straight pi ; Prove space that : minus left parenthesis straight i right parenthesis space space cos 4 straight A space plus space cos 4 straight B space plus space cos 4 straight C space equals space minus 1 plus 4 cos 2 straight A. cos 2 straight B. cos 2 straight C left parenthesis straight i right parenthesis space space cos squared straight A space plus space cos squared straight B space minus space cos squared straight C space equals space 1 minus 2 sinA. sinB. cosC

Asked by Olivia Adhikary | 4th Aug, 2014, 12:39: PM

Expert Answer:

G i v e n space A plus B plus C equals straight pi rightwards double arrow straight C equals straight pi minus left parenthesis straight A plus straight B right parenthesis  Consider space LHS LHS equals cos space 4 straight A space plus thin space cos space 4 straight B space plus space cos space 4 straight C equals 2 space cos space 2 left parenthesis straight A plus straight B right parenthesis space cos space 2 left parenthesis straight A minus straight B right parenthesis space plus thin space cos space 4 space left parenthesis straight pi minus left parenthesis straight A plus straight B right parenthesis right parenthesis equals space 2 space cos space 2 left parenthesis straight A plus straight B right parenthesis space cos space 2 left parenthesis straight A minus straight B right parenthesis space plus cos space 4 space left parenthesis straight A plus straight B right parenthesis equals 2 space cos space 2 left parenthesis straight A plus straight B right parenthesis space cos space 2 left parenthesis straight A minus straight B right parenthesis space plus 2 cos squared open parentheses straight A plus straight B close parentheses minus 1 equals 2 space cos space 2 left parenthesis straight A plus straight B right parenthesis open square brackets cos space 2 left parenthesis straight A minus straight B right parenthesis plus space cos space 2 left parenthesis straight A plus straight B right parenthesis close square brackets minus 1 equals 2 space cos space 2 left parenthesis straight pi minus straight C right parenthesis open square brackets 2 space cos space open parentheses 2 straight A close parentheses space cos space open parentheses 2 straight B close parentheses close square brackets minus 1 equals minus 1 space plus space 4 space cos space 2 straight A space cos space 2 straight B space cos space 2 straight C equals space RHS  Hence space Proved

Answered by Dharma Teja | 5th Aug, 2014, 09:13: AM

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