The given expression is equivalent to [tex]2\sin^{2}{3x}[/tex].
What is trigonometry identity?
When trigonometric functions are used in an expression or equation, trigonometric Identities come in handy.
One of the trigonometry identity is [tex]\cos2x=2\cos^{2} x-1[/tex].
What is the simplified expression for given expression?
In the given expression [tex]\cos6x[/tex] can be break as [tex]\cos(2\cdot3x)[/tex].
Now use the identity [tex]\cos2x=2\cos^{2} x-1[/tex] in the given expression.
[tex]1-\cos6x=1-2\cos^{2}{3x}+1[/tex]
[tex]=2(1-\cos^{2}{3x})[/tex]
Now use the identity [tex]1-\cos^{2}x=\sin^{2}x[/tex].
[tex]1-\cos6x=2\sin^{2}{3x}[/tex].
Therefore, the given expression is equivalent to [tex]2\sin^{2}{3x}[/tex].
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