Question

sec⁴ A − sec² A is equal to
(a)tan² A − tan⁴ A
(b)tan⁴ A − tan² A
(c)tan⁴ A + tan² A
(d)tan² A + tan⁴ A

Answer 1

Answer:

sec⁴ A − sec² A is equal to tan² A + tan⁴ A

Option d. is correct .

Step-by-step explanation:

Given :

sec⁴ A − sec² A

Taking sec² A  common

⇒  sec² A  (  sec² A  - 1 )  ... ( i )

We have Identity :

⇒  sec² A -  tan² A = 1

Rewrite it as

⇒  sec² A - 1 = tan² A ... ( ii )

⇒ sec² A = 1  +  tan² A ... ( iii )

Now from ( i )  and  ( ii ) we have

⇒ sec² A ( tan² A )

Putting sec² A values from ( iii )  we get

⇒ 1  +  tan² A (  tan² A )

⇒ tan² A + tan⁴ A

Thus we get answer .

Answer 2

$\boxed{\bold{\mathsf{SOLUTION }}}$

${sec}^{4} A - {sec}^{2} A \\ = > {sec}^{2} A[ {sec}^{2} A - 1] \: \: \: \: (taking \: sec {}^{2} A \: as \: \: common) \\ = > {sec}^{2} A \: \times {tan}^{2} A \: \: \: \:$

Let we assume tan^4 A + tan^2A ,we get

$= > {tan}^{4} A+ {tan}^{2} A\\ = > {tan}^{2} A[tan { }^{2} A +1]\\ = > {tan}^{4}A + {tan}^{2} A$

Hope it helps