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Sin^6x+cos^6x=1-3sin^2x×cos^2x |
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Answer» HI ,, LHS = sin^6 x + cos^6 = ( Sin² x )³ + ( cos² x )³ **************************** We know the algebraic identity, 1 ) a³ + b³ + 3AB( a + B ) = ( a + b )³ Or a³ + b³ = ( a + b )³ - 3ab( a + b ) 2 ) sin² x + cos² x = 1 ****************************** Here , a = sin² x , b = cos² x = (Sin²x + cos²x)³-3sin²xcos²x(sin² x+ cos²x) = 1 - 3sin²xcos²x = RHS I HOPE this helps you. : ) |
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