Question

can someone the solve the 77th one

Answer 1

Prove sin^6 a + cos^6 a =1-3sin^2 a cos^ a 

1)  sin^6 a + cos^6 a = (sin^2 a)^3 + (cos^2 a)^3
2) a^3 + b^3 = (a+b) (a^2 - ab + b^2)
3)  (sin^2 a)^3 + (cos^2 a)^3 = (sin^2 a + cos^2 a) (sin^4 a - sin^2 a* cos^2 a) + cos^4 a)
4) (sin^2 a + cos^2 a) = 1
5 ) sin^6 a + cos^6 a  = sin^4 a + cos^4 a - sin^2 a* cos^2 a
6) a^4 + b^4 = (a^2 +b^2 )- 2 a^2 b^2 
7) sin^4 a + cos^4 a -sin^2 a* cos^2 a =(sin^2 a + cos^2 a)-2sin^2 acos^2 a
8) sin^6 a + cos^6 a  = 1- 2sin^2 a cos^2 a - sin^2 a* cos^2 a
9) sin^6 a + cos^6 a  = 1- 3 sin^2 a cos^2 a