Prove the following: if `A+B=225^@`,then prove that `(frac(cotA)(1+cotA)).(frac(cotB)(1+cotB))=1/2`

Prove the following identities: (frac(cottheta)(cosectheta-1))=(frac(cosectheta+1)(cottheta))

Prove the following:If tanA=2tanB+cotB ,then 2tan(A-B)=cotB

Prove that sqrt(frac(cosecx-1)(cosecx+1))=(frac(1)(secx+tanx))

Prove the following identities: (frac(sintheta)(1+costheta))+(frac(1+costheta)(sintheta))=2cosectheta

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

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

If A+B=225^@ then cotA/(1+cotA).cotB/(1+cotB)=

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

Sove the following: In /_\ABC prove the following frac{c-bcosA}{b-c cosA} = frac{cosB}{cosC}

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