If
$$\displaystyle\sin \pi x= a_0+\sum_{n=1}^\infty a_n\cos(n\pi x)$$ for $0<x<1$,then $(a_0+a_1)\pi=?$
Solution I tried- I write $\sin \pi x=\sqrt(1-\cos^{2} \pi x$ which can be written as
$\displaystyle\sqrt(1-\frac{1+\cos2 \pi x}{2})$
further i am not gettiing how to solve
please help
Hint By the definition of Fourier cos series $$ a_0=\int_0^1\sin (\pi x) dx \\ a_1=\int_0^1 \sin (\pi x) \cos(\pi x) dx $$
Just calculate them