Answer:
To prove:
Cos⁴x - Sin⁴x = Cos2x
we get,
Consider, (Left hand side (LHS))
[tex]\cos^4x-\sin^4x[/tex]we know that,
[tex](a+b)(a-b)=a^2-b^2[/tex]Usind this formula we get,
[tex]\cos^4x-\sin^4x=(\cos^2x)^2-(\sin^2x)^2[/tex][tex]=(\cos^2x+\sin^2x)(\cos^2x-\sin^2x)[/tex]we know that,
[tex]\begin{gathered} \cos2x=\cos^2x-\sin^2x \\ \cos^2x+\sin^2x=1 \end{gathered}[/tex]Substitute the values we get,
[tex]=(1)(\cos2x)[/tex][tex]\cos^4x-\sin^4x=\cos2x[/tex]Hence proved.
