If `a cos 2 x+b sin 2 x = c` has `alpha` and `beta` as its roots, then prove that.

If a cos2x+b sin2x=c has alpha and beta as its roots,then prove that.

If a cos2 theta+b sin2 theta=chas alpha and beta as its roots,then prove that tan alpha+tan beta=(2ab)/(a+c)tan alpha+tan beta=(c-a)/(c+a)tan(alpha+beta)=(b)/(a)

If x=r sin alpha cos beta, y= r sin alpha sin beta and z= r cos alpha , prove that x^(2)+y^(2) + z^(2) = r^(2).

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that cos alpha cos beta = (c^(2) - b^(2))/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha sin beta = (c^(2)-a^(2))/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that sin alpha + sin beta = (2bc)/(a^(2) + b^(2))

If alpha, beta are solutions of a cos theta + b sin theta = c where a, b, c in R and a^(2) + b^(2) gt 0, cos alpha ne cos beta, sin alpha ne sin beta then prove that cos alpha + cos beta = (2ac)/(a^(2) + b^(2))

If x = cos alpha + i sin alpha , y = cos beta + i sin beta , prove that x^(m)y^(n)+1/(x^m y^n) = 2 cos (m alpha + n beta) .