Question

cos^6A+sin^6A=1/4(1+3cos^22A)

Answer 1

ok. here's the answer

Answer 2

Answer:

1/4 (1 + 3 cos^2 2A)

Step-by-step explanation:

L.H.S,

= cos^6 A + sin^6 A

= (cos^2 A)^3 + (sin^2 A)^3

= (cos^2 A + sin^2 A) (cos^4 A - cos^2 A sin^2 A + sin^4 A)

= (cos^2 A)^2 + (sin^2 A)^2 - cos^2 A sin^2 A

= (cos^2 A - sin^2 A)^2 + cos^2 A sin^2 A

= cos^2 2A + cos^2 A sin^2 A

= cos^2 2A + 1/4 (2 × cos A sin A)^2

= [4 cos^2 2A + sin^2 2A ] / 4

= [4 cos^2 2A + 1 - cos^2 2A] / 4

= 1/4 (1 + 3 cos^2 2A)

= R.H.S

[PROVED]