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

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

1/sec^2theta+1/(cosec^(2)theta)=1

(sec^2theta-1)(cosec^2theta-1)=1

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

"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)=

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)theta

Prove that : (i) 1+(cos^(2)theta)/(sin^(2)theta)-"cosec"^(2)theta=0 (ii) (1+tan^(2)theta)/("cosec"^(2)theta)=tan^(2)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-

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

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