# Write the given term $\cos 4\theta $ in terms of \[\cos \theta \].

Last updated date: 15th Mar 2023

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Answer

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Hint: Start by splitting the given terms and then apply the formula of \[\cos 2\theta \] in the above equation.

We have, \[\cos 4\theta \], we can apply the formula of \[\cos 2\theta = 2{\cos ^2}\theta - 1\],

\[\cos 4\theta = 2{\cos ^2}2\theta - 1\]

Again we will apply the same formula,

We get,

\[\cos 4\theta = 2{\left( {2{{\cos }^2}\theta - 1} \right)^2} - 1\]

\[\cos 4\theta = 8{\cos ^4}\theta - 8{\cos ^2}\theta + 1\]

Note: In these questions, the first step should be to split the given terms such that a formula can be applied to solve the question

We have, \[\cos 4\theta \], we can apply the formula of \[\cos 2\theta = 2{\cos ^2}\theta - 1\],

\[\cos 4\theta = 2{\cos ^2}2\theta - 1\]

Again we will apply the same formula,

We get,

\[\cos 4\theta = 2{\left( {2{{\cos }^2}\theta - 1} \right)^2} - 1\]

\[\cos 4\theta = 8{\cos ^4}\theta - 8{\cos ^2}\theta + 1\]

Note: In these questions, the first step should be to split the given terms such that a formula can be applied to solve the question

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