# PROVE THAT SIN^6X + COS^6X = 1

See below.Explanation:You could use the sản phẩm rule and the chain rule, but I find it more satisfying to rewrite the function before differentiating.From trigonometry: displaystylesinleft(2 heta ight)=2sinleft( heta ight)cosleft( heta ight) ...

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Equations like x= cos x or x=cot x generally don't have algebraic solutions. As such, we would first want to note that such an x exists (e.g., by the Intermediate Value Theorem) & then use ...
Are you familiar with the sản phẩm rule? f(x)=u(x)v(x)\ f'(x)=u'(x)v(x) + u(x)v'(x) In your case u(x)=cos(x), v(x)=sin(x). EDIT Sorry again for the typos, Here's what you should do. The ...
Lets bởi vì the first one. ag 1 y''-3y'-18y=x^2e^-2x The homogeneous solution is: y_h(x) = c_1 e^-3 x+c_2 e^6 x Next, lets vì chưng the calculations for the particular solution y_p=e^-2x(px^2+qx+r) ...
https://math.stackexchange.com/questions/1854885/find-inf-a-b-c-in-mathbb-c-int-pi-pixab-cos-xc-sin-x-2dx
Noting the oddness/evenness of the functions involved can lead us to: inf _a,b,cin mathbb Cint _<-pi,pi>|x+a+bcos x+csin x | ^2dx=inf _cin mathbb Cint _<-pi,pi>|x+csin x | ^2dx ...
( Expanded from the comments. ) The problem implies that all 3 vertices are at the same distance from the orthocenter, meaning that the orthocenter coincides with the circumcenter, which in turn ...
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