How to prove sec^4A-sec^2A=tan^4A+tan^2A

Question 1

How to prove sec4A-sec2A=tan4A+tan2A

Question 2

Solution:

Explanation: Use one of the Pythagorean identity namely,

sec2A=1+tan2A

LHS = sec4A−sec2A
=(sec2A)2−sec2A
=(1+tan2A)2−(1+tan2A)
=1+2tan2A+tan4A−1−tan2A

=tan4A+tan2A

= RHS

kratos · Answer 1 · 2020-11-05T09:17:44+0000

Solution:

Explanation: Use one of the Pythagorean identity namely,

sec2A=1+tan2A

LHS = sec4A−sec2A
=(sec2A)2−sec2A
=(1+tan2A)2−(1+tan2A)
=1+2tan2A+tan4A−1−tan2A

=tan4A+tan2A

= RHS

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