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If \(\cos { x+\sin { x=\frac { 1 }{ 2 } } } \), find the value of \(\tan { x } \).

NOTE: x belongs to 0 to \( \pi \)

If \(x_1,x_2,x_3...x_n\) are the roots of the equation \(1+x+x^2+x^3+...+x^n=0\) where \(n\) is a positive integer;

And ...

Consider a uniformly charged thin spherical shell of radius \(R\) carrying a uniform surface charge density \(\sigma\). It is made of two hemispherical shells held together by pressing with a ...

Let \(f(x) =k\cos x\). If the sum of coefficients of \(\cos x\) in the expansion of \(\left(1+f(x)\right)^n\) is \(\eta\) and the sum of ...

Let \(f(x)=1+2x+3x^2+4x^3+...+10x^9\) with \(x_1,x_2,x_3...x_9\) as the roots of \(f(x)=0\)

\(e_1=\sum x_1\)

\(e_2=\sum x_1x_2\)

...

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