Ritesh education_official

Find the equation whose roots are thenth powers of the roots of the equation x ^ 2 - 2x * cos theta + 1 = 0 Ritesh education_official

If (1+x)^n = C_{0} + C_{1}*x + C_{2} * x ^ 2 + C_{3} * x ^ 3 +...+C n x^ show that
(I) C 0 -C 2 +C 4 -...= 2 ^ (n / 2) * cos((n*pi)/4)
(ii) C 1 -C 3 +C 5 -...= 2 ^ (n / 2) * sin((n*pi)/4) Ritesh education_official

prove that one value of (a+b)+(a-ib)/n is 2 * (a ^ 2 + b ^ 2) ^ (m/(2n)) * cos(m/n * tan(- 1/b)) Ritesh education_official

If n be a positive integer, prove that (sqrt(3) + i) ^ n + (sqrt(3) - i) ^ n = 2 ^ (n + 1) * cos((n*pi)/6) Ritesh education_official

If n be a positive integer, prove that (1 + i) ^ n + (1 - i) ^ n = 2 ^ ((n + 2) / 2) * cos((n*pi)/4) Ritesh education_official

If (I + x)/(1 - x) = cos 2theta + i * sin 2theta , Prove that sx=itano. Ritesh education_official

If x + 1/x = 2cos alpha y + 1/y = 2cos beta, z + 1/z = 2cos gamma
prove that one of the values xyz ...+ 1 xyz... =2 cos( alpha+ beta+ gamma+...). Ritesh education_official

If x + 1/x = 2cos theta y + 1/y = 2cos phi prove that xy + 1/(xy) = 2cos(theta + phi) Ritesh education_official

If x + 1/x = 2cos theta show that x ^ n + 1/(x ^ n) = 2cos n*theta Ritesh education_official

If a = cos theta + i * sin theta b = cos phi + i * sin phi show that a ^ m * b ^ n + 1/(a ^ m * b ^ n) = 2cos(m*theta + n*phi) Ritesh education_official

If a = cos theta + i * sin theta b = cos phi + i * sin phi show that (a ^ m)/(b ^ n) + (b ^ n)/(a ^ m) = 2cos(m*theta - n*phi)
Ritesh education_official

If a = cos theta + i * sin theta b = cos phi + i * sin phi show that (a ^ 3)/(b ^ 3) + (b ^ 3)/(a ^ 3) = 2cos 3 * (theta - phi)
Ritesh education_official