`(sintheta+sectheta)^2+(costheta+cosectheta)^2=(1+sectheta cosectheta)^2`

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

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

If theta epsilon (0, pi/2) then the value of |((sintheta+cosectheta)^2, (sintheta- cosectheta)^2,1 ),((costheta+sectheta)^2, (costheta-sectheta)^2, 1),((tantheta+cottheta)^2, (tantheta-cottheta)^2, 1)|= (A) sintheta+costhetas+tantheta (B) 1 (C) 0 (D) 4

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

(sintheta+cosectheta)^2+(costheta+sectheta)^2=tan^2theta+cot^2+7 .

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

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

(1+cottheta-cosectheta)(1+tantheta+sectheta)=?

Prove that (sintheta+cosectheta)^2+(costheta+sectheta)^2ge9 .

Prove that (sintheta+cosectheta)^2+(costheta+sectheta)^2ge9 .