Question

ta4a+tan2=sec4a-sec2a​

Answer 1

Answer:

Step-by-step explanation:

Correct Question :-

Show that :-

$tan^4A+tan^2A=sec^4A-sec^2A$

To Prove :-

$tan^4A+tan^2A=sec^4A-sec^2A$

How To Do :-

Here we are asked to prove that 'tan⁴A + tan²A = sec⁴A - sec²A'. So by taking the L.H.S(tan⁴A + tan²A) and we can oberve that from this we can take 'tan²A' as the common term. After taking the common term we need to convert all 'tan' terms in the terms of 'sec' by using trigonometric identity.

Formula Required :-

1) sec²A - tan²A = 1

$\implies sec^2A=1+tan^2A$

$\implies tan^2A=sec^2A-1$

Solution :-

Taking L.H.S :-

$=tan^4A+tan^2A$

$=(tan^2A.tan^2A)+tan^2A$

Taking common :-

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

Substituting the values :-

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

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

$=sec^4A-sec^2A$

= R.H.S

Hence Proved.