Verifying Trigonometric Identities...6

[nycmathguy]

Section 5.2

This is part 7 not 6.

 

[MathLover1]

sin^4(x)+cos^4(x)=1-2cos^2(x)+2cos^4(x)

sin^2(x)sin^2(x)+cos^4(x)

=(1-cos^2(x))(1-cos^2(x))+cos^4(x)

=1-cos^2(x)-cos^2(x)+cos^4(x)+cos^4(x)

=1-2cos^2(x)+2cos^4(x)

 

[nycmathguy]

sin^4(x)+cos^4(x)=1-2cos^2(x)+2cos^4(x)

sin^2(x)sin^2(x)+cos^4(x)

=(1-cos^2(x))(1-cos^2(x))+cos^4(x)

=1-cos^2(x)-cos^2(x)+cos^4(x)+cos^4(x)

=1-2cos^2(x)+2cos^4(x)

I went to the moon and back with no verification. You drove down easy lane to verify this problem.
Is 52 correct?

What about the link below?

Verifying Trigonometric Identities...5