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

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

If (sin alpha + "cosec" alpha )^(2) + ( cos alpha + sec alpha )^(2)=k+ tan^(2) alpha + cot^(2) alpha then k=

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

If sin A , cos A and tan A are in G.P. then cot^(6) A- cot^(2) A =

( sin theta + " cosec " theta )^(2) + ( cos theta + sec theta )^(2)=

Prove that 1+cot^(2) theta = cosec^(2) theta