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

Sudheesh Singanamalla
114 Points
```										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

```
6 years ago
510 Points
```										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

```
6 years ago
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