Question

sin^6A+3sin^2Acos^2=1-cos^6A​

Answer 1

1 – 3sin2Acos2A

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