Why should we have \(\displaystyle{{\sin}^{{2}}{\left({x}\right)}}={\frac{{{1}-{\cos{{\left({2}{x}\right)}}}}}{{{2}}}}\) knowing that



Answered question


Why should we have sin2(x)=1cos(2x)2 knowing that sin2(x)=1cos2(x)?
Logically, can you not subtract cos2(x) to the other side from this Pythagorean identity sin2(x)+cos2(x)=1?
When I look up trig identities, however, it says sin2(x)=1cos(2x)2

Answer & Explanation

Jadyn Gentry

Jadyn Gentry

Beginner2022-03-24Added 12 answers

Notice that cos2(x)=(cos(x))2 is not the same thing as cos(2x). It is indeed true that sin2(x)=1cos2(x) and that sin2(x)=1cos(2x)2

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