Prove the following trigonometrical identities
`sec^2 theta + cosec^2 theta = sec^2 theta cosec^2theta`

Solve the following trigonometric equation : cosec^3 2 theta= 4 cosec 2 theta .

Solve the following trigonometric equation : cosec^2 theta= 2 cot theta .

Solve the following trigonometric equation : cosec theta= cot theta+sqrt3 .

tan^2theta+cot^2theta+2=sec^2thetacoses^2theta .

Prove the following identity : (sin theta+ cos theta) (sec theta+ cosec theta) =2+ sec theta cosec theta .

Prove the following identity : 2 sec^2 theta- sec^4 theta-2 cosec^2 theta+ cosec^4 theta= cot^4 theta-tan^4 theta .

Prove the following identity : (tan theta-cot theta)/ (sin theta cos theta)= sec^2 theta- cosec^2 theta .

Solve : sec theta-cosec theta =4/3 .

Solve the following trigonometric equation : tan theta+ sec theta= sqrt3 .

Solve the following trigonometric equation : sec theta- tan theta= sqrt3 .