Prove that `|alpha+sqrt(alpha^2-beta^2)|+|alpha-sqrt(alpha^2-beta^2)|= |alpha+beta|+|alpha-beta|` where `alpha,beta` are complex numbers.

Prove that | alpha+sqrt(alpha^(2)-beta^(2))|+| alpha-sqrt(alpha^(2)-beta^(2))|=| alpha+beta|+| alpha-beta| where alpha,beta are complex numbers.

Prove that: cos2alpha\ cos2beta+sin^2(alpha-beta)-sin^2(alpha+beta)=cos2(alpha+beta) .

Prove that alpha^(2)+beta^(2)=(alpha+beta)^(2)-2 alpha beta

Prove that: tan(alpha+beta)tan(alpha-beta)=(sin^2 alpha-sin^2 beta)/(cos^2 alpha-sin^2 beta)

Prove that: cos2 alpha cos2 beta+sin^(2)(alpha-beta)-sin^(2)(alpha+beta)=cos2(alpha+beta)

Prove that , tan(alpha+beta)tan(alpha-beta)=(sin^2alpha-sin^2beta)/(cos^2alpha-sin^2beta)

Prove that : cos^2alpha+cos^2(alpha+beta)-2cosalphacosbetacos(alpha+beta)=sin^2beta

Prove that 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)=cos2 alpha

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha

Prove that 2 sin^2 beta + 4 cos(alpha + beta) sin alpha sin beta + cos 2(alpha + beta) = cos 2alpha