Prove the following:`(frac(1)(tan3A-tanA))-(frac(1)(cot3A-cotA))=cot2A`

1/(tan3A-tan A)-1/(cot 3A-cot A)=

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

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

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

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

Prove the following: (frac(cotAcot4A+1) (cotAcot4A-1)) = (frac(cos3A) (cos5A))

Prove the following identities: (frac(1)(sectheta+tantheta))-(frac(1)(costheta))=(frac(1)(costheta))-(frac(1)(sectheta-tantheta))

Prove the following: (frac(cosx)(1+sinx))=(frac(cot(x/2)-1)(cot(x/2)+1))

Prove the following: (frac(1+tanx)(1-tanx))^2=(frac(tan(pi/4+x))(tan(pi/4-x)))

Prove the following: (frac(cosx+sinx)(cosx-sinx))-(frac(cosx-sinx)(cosx+sinx))=2tan2x