Prove the following identities: `2sec^2theta-sec^4theta-2cos e c^2theta+cos e c^4theta=cot^4theta-tan^4theta`

Explanation

LHS `=2 sec ^{2} theta-sec ^{4} theta-2 cosec^2 theta+cosec^4 theta `


`=(cosec^{4} theta-2 cosec^{2} theta)-(sec ^{4} theta-2 sec ^{2} theta) `


`=(cosec^{4} theta-2 cosec^{2} theta+1)-(sec ^{4} theta-2 sec ^{2} theta+1) `


`=(cosec^{2} theta-1)^{2}-(sec ^{2} theta-1)^{2} `


`=cot ^{4} theta-tan ^{4} theta `


={ RHS }