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prove that:- sin^6(A) + cos^6(A) = 1 - 3sin^2(A) cos^2(A)

prove that:-
sin^6(A) + cos^6(A) = 1 - 3sin^2(A) cos^2(A)

Grade:11

3 Answers

jagdish singh singh
173 Points
11 years ago

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ANKIT BATHLA
34 Points
11 years ago

sin6x+cos6x=(sin2x)3+(cos2x)+3sin2xcos2x(sin2x+cos2x)-3sin2xcos2x(sin2x+cos2x)             =(sin2x+cos2x)3-3sin2xcos2x                           =1-3sin2xcos2x        

Fawz Naim
37 Points
11 years ago

(A+B)^3=A^3+B^3+3AB(A+B)

=>A^3+B^3=(A+B)^3-3AB(A+B)

PUT A=SIN^2(A) AND B=COS^2(A)

SO A^3+B^3  WILL BE  SIN^6(A)+COS^6(A)

NOW SOLVE R.H.S. TO GET THE ANSWER

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