Question

Prove that
$cos^{6} \alpha +sin^{6} \alpha =1/4(1+3cos^22\alpha )=1/8(5+3cos4\alpha )$cos$cos^{6} \alpha +sin^{6} \alpha =1/4(1+3cos^22\alpha )=1/8(5+3cos4\alpha )$

Answer 1

Answer:

Step-by-step explanation:

Given sin6A + cos6A

 

sin6A + cos6A = (sin2A)3 + (cos2A)3

 

(a + b)3 = a3+ b3 + 3ab

 

(sin2A + cos2A)3 = (sin2A+cos2A)3 – 3sin2Acos2A

 

sin2A + cos2A = 1

 

(sin2A + cos2A)3 = 1 – 3sin2Acos2A

 

sin6A + cos6A = 1 – 3sin2Acos2A