Question

prove that sec⁴A - sec²A = tan²A + tan⁴A​

Answer 1

Step-by-step explanation:

LHS =sec^4A - sec^2A

=sec^2A (sec^2A-1)

=sec^2A .tan^2A {because sec^2A-tan^2A=1 }

=(1+tan^2A) tan^2A

=tan^4A+tan^2A =RHS

Answer 2

To prove:

sec⁴A - sec²A = tan² A + tan⁴ A

LHS= sec⁴A - sec² A

= sec²A (sec²A - 1 )

= (1 + tan²A) ( tan² A ). [Using sec²= 1+ tan² ]

= tan² A + tan⁴ A

= RHS

HENCE PROVED.