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

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

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

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

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

Prove the following: (frac(2cos2A+1)(2cos2A-1))=tan(60^@+A)tan(60^@-A)

Prove the following: (frac(1-cos2theta+sin2theta)(1+cos2theta+sin2theta))=tantheta

Select and write the correct answer from the given alternatives in each of the following: (frac(cos12-sin12)(cos12+sin12))+(frac(sin147)(cos147)) =

Prove the following: sin18^@cos39^@+sin6^@cos15^@=sin24^@cos33^@

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

Prove the following: (frac(1-cos2theta)(1+cos2theta))=tan^2theta