Verify the following:`(frac(1+tan45^@tan60^@)(tan45^@-tan60^@))=(frac(1+sqrt3)(1-sqrt3))`

Verify the following: (frac(tan60^@+sec60^@)(tan60^@-sec60^@))=-(7+4sqrt3)

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

tan20^@+tan40^@+sqrt3tan20^@tan40^@=

Prove the following: tanA+tan(60^@+A)+tan(120^@+A)=3tan3A

Prove the following: tan20^@tan80^@cot50^@=sqrt3

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

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

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

Prove the following identities: (frac(tan^3theta)(1+tan^2theta))+(frac(cot^3theta)(1+cot^2theta))=secthetacosectheta-2sinthetacostheta

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