Q. Let n be an odd integer if `sin ntheta=sum_(r=0)^n(b_r)sin^rtheta`, for every value of theta then `b_0 and b_1`---

Find the sum sum_(r=0)^n^(n+r)C_r .

The value of sum_(r=0)^n(a+r+a r)(-a)^r is equal to

sin^2 n theta- sin^2 (n-1)theta= sin^2 theta where n is constant and n != 0,1

If theta in (pi//4, pi//2) and sum_(n=1)^(oo)(1)/(tan^(n)theta)=sin theta + cos theta , then the value of tan theta is

Statement1: if n in Na n dn is not a multiple of 3 and (1+x+x^2)^n=sum_(r=0)^(2n)a_r x^r , then the value of sum_(r=0)^n(-1)^r a r^n C_r is zero Statement 2: The coefficient of x^n in the expansion of (1-x^3)^n is zero, if n=3k+1orn=3k+2.

If (4x^(2) + 1)^(n) = sum_(r=0)^(n)a_(r)(1+x^(2))^(n-r)x^(2r) , then the value of

If x = sum_(n = 0)^(infty) cos ^(2n) theta, " "y = sum_(n = 0)^(infty) sin^(2n) theta and z = sum_(n = 0)^(infty) cos^(2n) theta sin^(2n)theta, 0 lt theta lt (pi)/(2) , then show that xyz = x + y + z [ Hint : use the formula 1 + x + x^(2) + x^(3) +... =(1)/(1 - x) , where |x| lt 1 ]

Let A={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin theta , 1 )]:} ,"where" 0 letheta le 2pi , Then

If the sum of the series sum_(n=0)^oor^n ,|r|<1 is s , then find the sum of the series sum_(n=0)^oor^(2n) .