(sin³x)²+(cos³x)²=?? 5
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(sin³x)²+(cos³x)²
=(sin²x)³+(cos²x)³
=(sin²x)³+3(sin²x)²cos²x+3sin²x(cos²x)²+(cos²x)³-3sin²xcos²x(sin²x+cos²x)
=(sin²x+cos²x)³-3sin²xcos²x
=1³-(3/4)(2sinxcosx)²
=1-(3/4)sin²2x
=1-(3/8)(1-cos4x)
=(3/8)cos4x+(5/8)
所以 (sin³x)²+(cos³x)²=(3/8)cos4x+(5/8)
希望能帮到你!
=(sin²x)³+(cos²x)³
=(sin²x)³+3(sin²x)²cos²x+3sin²x(cos²x)²+(cos²x)³-3sin²xcos²x(sin²x+cos²x)
=(sin²x+cos²x)³-3sin²xcos²x
=1³-(3/4)(2sinxcosx)²
=1-(3/4)sin²2x
=1-(3/8)(1-cos4x)
=(3/8)cos4x+(5/8)
所以 (sin³x)²+(cos³x)²=(3/8)cos4x+(5/8)
希望能帮到你!
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