prove that
sin 6x + cos6 x = 1 - 3 sin2 x cos2x
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Step-by-step explanation:
(sin²x+cos²x)²=sin⁴x+cos⁴x+2sin²xcos²x
1=sin⁴x+cos⁴x+2sin²xcos²x
sin⁴x+cos⁴x=1-2sin²xcos²x
sin⁶x+cos⁶x
=(sin²x)³+(cos²x)³
=(sin²x+cos²x)(sin⁴x-sin²xcos²x+cos⁴x)
=(1)(sin⁴x+cos⁴x-sin²xcos²x)
=(1-2sin²xcos²x-sin²xcos²x)
=(1-3sin²xcos²x)
Hence proved
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Answer:
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