sin6A+cos6A=1-3sin2Acos2A
sin6A+cos6A=1-3sin2Acos2A
priyanshi joshi , 11 Years ago
Grade
Trigonometry> sin 6 A+cos 6 A=1-3sin 2 Acos 2 A...
2 AnswersY RAJYALAKSHMI
sin6A + cos6A = (sin2A)3 + (cos2A)3 = (sin2A + cos2A)(sin4A – sin2Acos2A + cos4A)
= 1 (sin4A – sin2Acos2A + cos4A + 2sin2Acos2A – 2sin2Acos2A)
= (sin2A + cos2A) – 3sin2Acos2A
= 1 – 3sin2Acos2A
BShankar
sin^2A + cos^2A =1
Cubing on both sides
(sin^2A+cos^2A)^3=1^3
(sin^2A)^³+(cos^2A)^3 + 3sin^2Acos^2A(sin^2A+cos^2A)=1
sin^6A+cos^6A+3sin^2Acos^2A(1)=1
sin^6A+cos^6A=1-3sin^2Acos^2A
Hence, proved.
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