Prove `sec^2 theta = 1+ tan^2 theta`

Prove that- sec^2theta-1-tan^2theta=0

Prove that: 1/(sec theta - tan theta) = sec theta + tan theta .

Prove that: (sec theta + tan theta -1)/(tan theta - sec theta +1) = (cos theta)/(1- sin theta)

Prove that sec theta + tan theta = tan (pi/4 + theta/2)

Prove that sec theta + tan theta = (cos theta)/(1-sin theta)

Prove that: sec theta + tan theta = (cos theta)/(1-sin theta) .

Prove that (i) ("cosec"^(2) theta-1 ) tan^(2) theta =1 " " (ii) (sec^(2) theta -1)(1- "cosec"^(2) theta )=-1

Prove that (sec^(2)theta-tan theta)/(sec^(2)theta+tan theta) lies between 3 and (1)/(3).

Prove :sec^(6)theta=tan^(6)theta+3tan^(2)theta sec^(2)theta+1

Prove that (1)/(sec theta - tan theta) = sec theta + tan theta