which of the following are true?

cos⁴A - cos²A = LHS

cos²A(cos²A - 1) = (1 - sin²A)(-sin²A) = sin⁴A - sin²A = RHS 

First identity is true.

sin⁶A + cos⁶A  = 1 - 3sin²Acos²A

sin⁶A + cos⁶A  + 3sin²Acos²A = 1

 sin⁶A + cos⁶A  + 3sin²Acos²A(sin²A + cos²A) = 1

(sin²A + cos²A)³ = 1

1 = 1

Second identity is also true.

sec⁴A + sec²A = tan⁴A + tan²A

sec⁴A + sec²A = tan²A(tan²A + 1)

 

sec⁴A + sec²A = tan²A(sec²A)

sec⁴A + sec²A = (sec²A - 1)(sec²A)

sec⁴A + sec²A = sec⁴A - sec²A

Third identity is not true.

cot⁴A - 1 = cosec⁴A - 2cosec²A

cot⁴A - 1 = cosec²A(cosec²A - 2)

 cot⁴A - 1 = (1 + cot²A)(cot²A - 1)

 cot⁴A - 1 =  cot⁴A - 1

This identity is also true.

 

Regards,

Team,

TopperLearning.