if cos^4A-sin^4A=x, find cos^6A-sin^6A in terms of x

cos^4 A - sin^4 A = x

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

==> cos^2 A - sin^2 A = x

cos^6 A - sin^6 A = (cos^2 A)^3 - (sin^2 A)^3 = (cos^2 A - sin^2 A)(cos^4 A + sin^4 A + sin^2 A. cos^2 A)

= x . ( 1 + sin^2 A .cos^2 A)

= x + x.sin^2 A.cos^2 A

Please approve !

Approved

cos⁴A-sin⁴A = (cos²A+sin²A)(cos²A-sin²A) = x

               = (cos²A-sin²A) = x                                                 (cos²A-sin²A = cos2A)

               cos2A = x      ..........1

              sin2A = (1-x²)^1/2   ............2

we have to find the value of cos⁶A - sin⁶A = P

 P = cos⁶A - sin⁶A

    =(cos²A+sin²A)(cos⁴A + sin⁴A-cosAsinA)

    =(sin⁴A+cos⁴A-cosAsinA)

    = [ 1 + cos²2A -sin2A]/2

    = [ 1+ x² - (1-x²)^1/2]/2

this is the value of expression

Approved