已知sina+cosa=m,(|m|
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1: solution:
sin^3a + cos^3a = (sin(a) + cos(a))( sin^2(a) + cos^2(a) - sin(a) * cos(a))
= (sin(a) + cos(a))( 1 - sin(a) * cos(a)) = m ( 1 - sin(a) * cos(a)) )
m^2 = (sina + cosa)^2 = 1 + 2 * sina * cosa
sina * cosa = ( m^2 - 1 ) / 2
so sin^3a + cos^3a = m * ( 1 - ( m^2 - 1 ) / 2 ) = m * (3 - m^2) /2
2: solution
sin^4a + cos^4a = ( sin^2a + cos^2a )^2 - 2 * sin^2a * cos^2a
= 1 - 2 * (m^2 - 1)^2 / 4 = ...
sin^3a + cos^3a = (sin(a) + cos(a))( sin^2(a) + cos^2(a) - sin(a) * cos(a))
= (sin(a) + cos(a))( 1 - sin(a) * cos(a)) = m ( 1 - sin(a) * cos(a)) )
m^2 = (sina + cosa)^2 = 1 + 2 * sina * cosa
sina * cosa = ( m^2 - 1 ) / 2
so sin^3a + cos^3a = m * ( 1 - ( m^2 - 1 ) / 2 ) = m * (3 - m^2) /2
2: solution
sin^4a + cos^4a = ( sin^2a + cos^2a )^2 - 2 * sin^2a * cos^2a
= 1 - 2 * (m^2 - 1)^2 / 4 = ...
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