Prove that \sin^{2}x-\cos^{2}=1-2cos^{2}x

pavitorj6 2021-11-22 Answered
Prove that \(\displaystyle{{\sin}^{{{2}}}{x}}-{{\cos}^{{{2}}}=}{1}-{2}{{\cos}^{{{2}}}{x}}\)

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Expert Answer

Mary Moen
Answered 2021-11-23 Author has 850 answers
Look, we have:
\(\displaystyle{{\sin}^{{{2}}}-}{{\cos}^{{{2}}}{x}}={{\sin}^{{{2}}}{x}}+{\left({{\cos}^{{{2}}}{x}}-{{\cos}^{{{2}}}{x}}\right)}-{{\cos}^{{{2}}}{x}}={\left({{\sin}^{{{2}}}{x}}+{\cos}^{{{2}}}\right)}-{2}{{\cos}^{{{2}}}{x}}={1}-{2}{{\cos}^{{{2}}}{x}}\)
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Ceitheart
Answered 2021-11-24 Author has 906 answers

Just start with \(\displaystyle{{\sin}^{{{2}}}{x}}+{{\cos}^{{{2}}}{x}}={1}\) and subtract
\(2\cos^{2}x\) from both sides. And here you go!

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