Question

please solve this
$\cos( ^{6} ) a + \sin(^{6} ) a = 1 - 3 \sin( ^{2} ) \cos(^{2} ) a$
pls don't mess its important ​

Answer 1

Answer:

L.H.S. = cos⁶a + sin⁶a

= (cos²a + sin²a) (cos⁴a - sin²a cos²a + sin²a)

= (sin⁴a + cos⁴a) - sin²a cos²a

= 1 - 2sin²a cos²a - sin²a cos²a

= 1 - 3sin²a cos²a

= R.H.S.

Hence proved.