Question

sin power 6 theta + cos power 6 theta equals to 3 sin square theta into cos square theta​

Answer 1

Correct Question :-- Prove that , sin⁶A+cos⁶A = 1 - 3.sin²A.cos²A

Solution :--

Taking LHS we get , ,

= sin⁶A+cos⁶A

= (sin²A)³ + (cos²A)³

[ Using a³ + b³ = (a+b)³ - 3ab(a+b) ]

= ( sin²A+cos²A)³ - 3(sin²A.cos²A)(sin²A+cos²A)

[ using sin²A + cos²A = 1 we get, ]

= 1 - 3(sin²A.cos²A)(1)

= 1 - 3(sin²A.cos²A) = RHS .

✪✪ Hence Proved ✪✪