Question

prove that sin six thita + cos six thita = 1-3 sin square thita.cos square thita.

Answer 1

to prove
 sin6ө + cos6ө =1-3sin2өcos2ө
(sin²Ф)³ + (cos ²Ф)³
∴          a³+b³=  (a+b)³-3ab(a+b)

(sin²Ф + cos²Ф)³ - 3(sin²Ф * cos²Ф)(sin²Ф + cos²Ф)
acc. to sin²Ф + cos²Ф = 1

(1)³-3(sin²Ф * cos²Ф)(1)
1-3(sin²Ф * cos²Ф)