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Show algebraically how to confirm that cos2x = cos2x - sinx using the sum and difference identities. Show all steps....

Show Algebraically How To Confirm That Cos2x Cos2x Sinx Using The Sum And Difference Identities Show All Steps class=

Sagot :

We are to prove that,

[tex]\cos 2x=\cos ^2x-\sin ^2x[/tex]

Apply the angle-sum identity for cosine to cos (x + x),

Therefore,

[tex]\cos 2x=\cos (x+x)[/tex][tex]\begin{gathered} \cos (x+x)=\cos x\cos x-\sin x\sin x \\ \cos (x+x)=\cos x\times\cos x-\sin x\times\sin x \\ \cos (x+x)=\cos ^2x-\sin ^2x \end{gathered}[/tex]

Hence, with the above prove it has been shown that they are equal.

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