Question

Prove thatsin^6theta + cos^6theta +3sin^2theta ×cos^2theta =1

Answer 1

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