Question

( ii) Express cos^6 A+sin^6A in terms of sin 2A.​

Answer 1

Answer:

$( {cos}^{2} x) {}^{3} + ( {sin}^{2} x) {}^{3} = ( {cos}^{2} x + {sin}^{2} x) {}^{3} - 3 {cos}^{2} x {sin}^{2} x( {cos}^{2} x + {sin}^{2} x) = 1 - \frac{3}{4} (2sinx \: cosx) {}^{2} = 1 - \frac{3}{4} {sin}^{2} 2x.$