Evaluate the following limit : `(lim)_(alpha->beta)[(sin^2alpha-sin^2beta)/(alpha^2-beta^2)]\ \ `

lim_(alpha to beta)[(sin^(2)alpha-sin^(2)beta)/(alpha^(2)-beta^(2))] is equal to

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

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

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

If cos(alpha+beta)=0 then sin^(2)alpha+sin^(2)beta

Simplify 2sin^(2)beta+4cos(alpha+beta)sin alpha sin beta+cos2(alpha+beta)

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