Prove thatsin^6theta + cos^6theta +3sin^2theta ×cos^2theta =1
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Heya!!
a³ + b³ = ( a + b )³ - 3ab ( a + b )
Sin² x + Cos² x = 1
_______________________________
Exp:-
( Sin² x + Cos² x )³ - 3 Sin² x × Cos² x
× ( Sin² x + Cos² x ) + 3 Sin² x × Cos² x
=>
(1)³ - 3 Sin² x × Cos² x (1) + 3Sin²x Cos²x
=>
( 1 )³
= 1
a³ + b³ = ( a + b )³ - 3ab ( a + b )
Sin² x + Cos² x = 1
_______________________________
Exp:-
( Sin² x + Cos² x )³ - 3 Sin² x × Cos² x
× ( Sin² x + Cos² x ) + 3 Sin² x × Cos² x
=>
(1)³ - 3 Sin² x × Cos² x (1) + 3Sin²x Cos²x
=>
( 1 )³
= 1
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