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

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

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

( ( 1 + tan ^ 2 A )/( 1 + cot ^ 2 A )) = (( 1 - tan A)/ ( 1 - cot A )) ^ 2 = tan ^ 2 A

( cos A - sin A + 1 ) / ( cos A + sin A - 1 ) = cosec A + cot A cosec A + cot A , = using the identity cosec ^ 2 A = 1 + cot^ 2 A .

( 5 cos ^ 2 60^ @ + 4 sec ^ 2 30 ^@ -tan ^ 2 45 ^@ ) /( sin ^ 2 30^@ + cos ^ 2 30 ^@ )

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

If 3 cot A = 4 , check whether (1 - tan ^ 2 A ) /( 1 + tan ^ 2 A ) = cos ^ 2 A - sin ^ 2 A or not

(sin 30 ^@ + tan 45 ^@- cosec 60 ^@ ) /( sec 30 ^@ + cos 60 ^@ + cot 45 ^@ )

If sin A = cos A , find the value of 2tan^(2)A + sin^(2)A +1 .

( 1 + tan theta + sec theta ) ( 1 + cot theta - cosec theta ) =