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

Prove the following: (frac(sec2A-1)(sec4A-1))=frac(tanA)(tan4A)

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

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

Prove the following: (frac(sintheta)(1+costheta))=tan(theta/2)

Prove the following: (frac(2cos4x+1)(2cosx+1))=(2cosx-1)(2cos2x-1)

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

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

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

Prove the following: (frac(cot6A-tan2A)(cot6A+tan2A))=(cos8A)/(cos4A)

Select and write the correct answer from the given alternatives in each of the following: (frac(1-tan^2 60^@)(1+tan^2 60^@)) =………….