Prove that `(cosec A - sin A ) (sec A -cos A) = ( 1)/( tan A +cot A) `

Prove that cos A/(1 - tan A) + sin A /(1 - cot A) = sin A + cos A

Show that (cot A - cos A)/(cot A + cos A) = ( cosec A - 1)/(1 + cosec A)

Prove that ( sin A+ cosec A)^2+(cos A+sec A)^2=7+tan^2 A+ cot^2 A .

Prove that ( 1+ sec A)/( sec A) =(sin ^(2) A)/( 1-cos A)

If A is not an integral multiple of (pi)/(2) , prove that (i) tan A + cot A= 2 cosec 2 A (ii) cot A - tan A = 2cot 2A

Prove that sqrt((cosec A + 1)/(cosec A - 1)) - sqrt((cosec A - 1)/(cosec A + 1)) = 2tan A

Prove that (sin A +cosec A) ^(2) +(cos A +sec A) ^(2) =7+ tan ^(2) A +cot ^(2) A

("cosec " theta - sin theta ) ( sec theta - cos theta ) ( tan theta + cot theta ) =

Prove that (sin theta - cos theta + 1)/(sin theta + cos theta - 1) = (1)/(sec theta - tan theta) using the identity sec^(2) theta = 1 + tan^(2) theta .

Prove that (1+cot theta -"cosec" theta ) (1+ tan theta + sec theta )=2 .