A circle is inscribed in an n-sided regular polygon `A_1, A_2, …. A_n` having each side a unit for any arbitrary point P on the circle, pove that `sum_(i=1)^(n)(PA_i)^2=n(a^2)/(4)(1+cos^2((pi)/(n)))/(sin^2((pi)/(n)))`

sum_(n=1)^(20)[sin((2n pi)/(21))-i cos((2n pi)/(21))]=

The area of the circle and the area of a regular polygon of n sides and of perimeter equal to that of the circle are in the ratio of tan((pi)/(n)):(pi)/(n)(b)cos((pi)/(n)):(pi)/(n)sin(pi)/(n):(pi)/(n)(d)cot((pi)/(n)):(pi)/(n)

If n is an integer then show that (1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos(n pi)/(2)

I_(n) is the area of n sided regular polygon inscribed in a circle of unit radius and O_(n) be the area of the polygon circumscribing the given circle, prove that I_(n)=O_(n)/2(1+sqrt(1-((2I_(n))/n)^(2)))

The sum of radii of inscribed and circumscribed circles of an n sided regular polygon of side a is

The value of lim_(n rarr oo)sum_(i=1)^(n)(i)/(n^2)sin((pi i^(2))/(n^(2))) is equal to

If r is the radius of inscribed circle of a regular polygon of n-sides ,then r is equal to

If sum_(i=1)^(2n)sin^(-1)x_(i)=n pi then find the value of sum_(i=1)^(2n)x_(i)

" *.i).i) If "n" is an integer then show that "(1+i)^(2n)+(1-i)^(2n)=2^(n+1)cos(n pi)/(2)

A circle of radius r is inscribed in a regular polygon with n sides (the circle touches all sides of the polygon). If the perimeter of the polygon is p, then the area of the polygon is