Prove the following:`(frac(sin(A-B))(cosAcosB))+(frac(sin(B-C))(cosBcosC))+(frac(sin(C-A))(cosCcosA))=0`

Prove the following: (frac(sin3x)(cosx))+(frac(cos3x)(sinx))=2cot2x

Prove the following: sin18^@=(frac(sqrt5-1)(4))

Prove the following: (frac(sin5x-2sin3x+sinx)(cos5x-cosx))=tanx

Prove the following: (frac(tan5A-tan3A)(tan5A+tan3A))=(frac(sin2A)(sin8A))

Prove the following: (frac(cos9x-cos5x)(sin17x-sin3x))=(frac(-sin2x)(cos10x))

Prove the following : (frac(cos11-sin11)(cos11+sin11))=cot56

Prove the following: frac(sin(x+y))(sin(x-y))=frac(tanx+tany)(tanx-tany)

Prove the following: sqrt(frac(1+sin2x)(1-sin2x))=tan(pi/4+x)

Solve the following: If (frac(cos(A+B))(cos(A-B)))=(frac(sin(C+D))(sin(C-D))) prove that tanA.tanB.tanC+tanD=0

Prove the following: (frac(sin2x+sin2y)(sin2x-sin2y))=(frac(tan(x+y))(tan(x-y)))