Question

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

Answer 1

We are to prove that,

`\cos 2x=\cos ^2x-\sin ^2x`

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

Therefore,

`\cos 2x=\cos (x+x)`
`\begin{gathered} \cos (x+x)=\cos x\cos x-\sin x\sin x \\ \cos (x+x)=\cos x*\cos x-\sin x*\sin x \\ \cos (x+x)=\cos ^2x-\sin ^2x \end{gathered}`

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