Question

Sec⁴ A - Sec² A =

(a) tan² A - tan⁴ A
(b) tan⁴ A - tan² A
(c) tan⁴ A + tan² A
(d) tan² A + tan⁴ A​

Answer 1

Answer:

(b) tan⁴ A - tan² A

Step-by-step explanation:

Sec⁴ A - Sec² A

= 1+tan⁴ A - 1+tan² A

=tan⁴ A - tan² A

Answer 2

Answer:

b) tan⁴A - tan²A

Step-by-step explanation:

Given: sec⁴A - sec²A

To find: the value of sec⁴A - sec²A

Solution: Let's say that the value of sec⁴A - sec²A is x.

From trigonometry formulas we know that,

• sin²Ø + cos²Ø = 1
• tan²Ø + 1 = sec²Ø
• 1 + cot²Ø = cosec²Ø

From above we can say that sec²A = tan²A + 1

Now,

→ sec⁴A - sec²A = (tan⁴A + 1) - (tan²A + 1)

→ sec⁴A - sec²A = tan⁴A + 1 - tan²A - 1

+1 and -1 cancel out,

→ sec⁴A - sec²A = tan⁴A - tan²A

Therefore, the value of sec⁴A - sec²A is tan⁴A - tan²A.

Hence, option b) tan⁴A - tan²A is correct.