Prove: `(sectheta+costheta)(sectheta-costheta)=tan^2theta+sin^2theta`

For any real theta , (csc theta - sin theta)(sectheta-costheta)(tan theta+cot theta)=......

Prove that ("cosec "theta-sintheta)(sectheta-costheta)(tantheta+cottheta)=1

Prove that (sectheta +cosectheta)(sintheta+costheta)=2+secthetacosectheta

Prove the following identities: (cosec theta-sintheta)^2+(sectheta-costheta)^2-(tantheta-cottheta)^2=1

What is the value of (sectheta-costheta)("cosec"theta-sintheta)(cottheta+tantheta) ?

Prove: (1+sectheta)/(sectheta)=(sin^2theta)/(1-costheta)

Prove the following: (sintheta+cosectheta)^2+(costheta+sectheta)^2=Tan^2theta+cot^2theta+7

(i) (sec theta-cos theta)(cosectheta-"sin"theta)=(1)/("tan"theta+cottheta) (ii) ("sin"theta+sectheta)^(2)+(costheta+cosectheta)^(2)=(1+secthetacosectheta)^(2)

Prove: (1+costheta-sin^2theta)/(sintheta(1+costheta))= cottheta

Prove the following (sintheta +cosectheta) ^2+(costheta+sectheta) ^2=7+tan^2theta+cot^2theta