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(sin3x)(cosx))+(frac(cos3x)(sinx))=2cot2x

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

If ( cos (A+B))/( cos (A-B)) =( sin (C+D))/( sin (C -D)) then prove that tan A tan B tan C + tan D=0 ................. A) 0 B) -1 C) sqrt3 D) 1

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

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

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

Prove the following: (frac(cos2theta)(1+sin2theta))=tan(pi/4-0)

Prove the following: (frac(cos27^@+sin27^@)(cos27^@-sin27^@))=tan72^@

Solve the following: If frac{sinA}{sinC} = frac{sin(A-B)}{sin(B-C)} , then show that a^2, b^2, c^2 are in A.P.

Prove the following: frac(cos15^@-sin15^@)(cos15^@+sin15^@)=1/sqrt3