ACCORDING TO THE QUES,
![\[LHS\text{ }=\text{ }cos\text{ }4x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-847c596c0111f058a5feded2bf6c33c0_l3.png "Rendered by QuickLaTeX.com")
We can compose it as
![\[=\text{ }cos\text{ }2\left( 2x \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0179b3ae1018c2252904fc2c5f466528_l3.png "Rendered by QuickLaTeX.com")
Utilizing the equation
![\[cos\text{ }2A\text{ }=\text{ }1\text{ }\text{ }2\text{ }sin2\text{ }A\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6e77cecc0fdc9ffe6a1362d4fe46fd8b_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }1\text{ }\text{ }2\text{ }sin2\text{ }2x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-ca39b38b3492243b16adb1a50fb3b652_l3.png "Rendered by QuickLaTeX.com")
Again by utilizing the equation
![\[sin2A\text{ }=\text{ }2sin\text{ }A\text{ }cos\text{ }A\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7e4877a9e10ccb8a02717a9b7fbf7603_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }1\text{ }\text{ }2\left( 2\text{ }sin\text{ }x\text{ }cos\text{ }x \right)\text{ }2\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3cceb0f0436918db97bbedff7a95f530_l3.png "Rendered by QuickLaTeX.com")
So we get
![\[=\text{ }1\text{ }\text{ }8\text{ }sin2x\text{ }cos2x\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-6ccd122841527fc7f6355cb33c2c546e_l3.png "Rendered by QuickLaTeX.com")
![\[=\text{ }R.H.S.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-da176931c085962608290d7f194ed72b_l3.png "Rendered by QuickLaTeX.com")
ACCORDING TO THE QUES,
We can compose it as
Utilizing the equation
Again by utilizing the equation
So we get
