Question -
Answer -
Let us consider LHS: sin6 x+ cos6 x
(sin2 x) 3 +(cos2 x) 3
By using the formula, a3 + b3 =(a + b) (a2 + b2 – ab)
(sin2 x + cos2 x)[(sin2 x) 2 +(cos2 x) 2 –sin2 x cos2 x]
By using the formula, sin2 x + cos2 x= 1 and a2 + b2 = (a + b) 2 –2ab
1 × [(sin2 x + cos2 x) 2 – 2sin2 xcos2 x – sin2 x cos2 x
12 –3sin2 x cos2 x
1 – 3sin2 x cos2 x
= RHS
∴LHS = RHS
Hence proved.