[" 24.cosce "A+cosec B)^(2)-(cot B-sec A)^(2)=2tan A cot B(cosec A+sec B)],[" 25."(tan A)thetaquad cot theta]

Prove the following identities: (1+tan A tan B)^(2)+(tan A-tan B)^(2)=sec^(2)A sec^(2)B(tan A+csc B)^(2)-(cot B-sec A)^(2)=2tan A cot B(csc A+sec B)

(sec theta+csc theta)^(2)-(tan theta+cot theta)^(2)=

Prove that sqrt( sec^(2) theta + "cosec"^(2) theta )= tan theta + cot theta .

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

Prove that : (sec A - tan A)/ (cosec A + cot A) = (cosec A - cot A)/ (sec A + tan A)

Prove each of the following identities : (i) ("cosec"theta + cot theta )/("cosec"theta - cot theta ) = ("cosec" theta + cot theta)^(2) = 1+2cot^(2) theta + 2"cosec" theta cot theta (ii) (sec theta + tan theta ) /( sec theta - tan theta) =(sec theta + tan theta )^(2) = 1+ 2tan^(2) theta + 2 sec theta tan theta

The value of cosec ^(2) theta cot ^(2) theta - sec ^(2) theta tan ^(2) theta -(cot ^(2) theta- tan ^(2) theta) (sec ^(2) theta cosec ^(2) theta -1) is-

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

If sec theta - cosec theta = 0 ,then the value of tan theta + cot theta is