Prove the following identities:`(secA+cosA)(secA-cosA)=tan^2A+sin^2A`

Prove the following identities: (cos^2A-1)(cot^2A+1)=-1

Prove the following: cosecA-2cot2A.cosA=2sinA

Prove the following identities: (1+cottheta-cosectheta)(1+tantheta+sectheta)=2

Prove the following: sqrt2cos(pi/4-A)=cosA+sinA

Prove the following identities: (1+tan^2A)+(1+frac(1)(tan^2A))=frac(1)(Sin^2A-Sin^4A)

Prove the following: sin(A+B).sin(A-B)=cos^2B-cos^2A

Prove the following identities: (sintheta+sectheta)^2+(costheta+cosectheta)^2=(1+cosecthetasectheta)^2

Prove the following: tan pi/8=sqrt2-1

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

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