Question

sec⁴A(1- sin⁴A)-2tan²A​

Answer 1

$\huge\boxed{\bf sec^4A(1- sin^4A)-2tan^2A=1}$

sec⁴A(1-sin⁴A)-2tan²A

⇒ sec⁴A - sec⁴A sin⁴A - 2tan²A

⇒ sec⁴A - sin⁴A(1/cos⁴A) - 2tan²A

⇒ sec⁴A - tan⁴A - 2tan²A

⇒ {(sec²A)² - (tan²A)²} - 2tan²A

⇒ (sec²A + tan²A)(sec²A - tan²A) - 2tan²A

[∵ sec²A-tan²A=1]

⇒ sec²A + tan²A - 2tan²A

⇒ sec²A - tan²A

⇒ 1

$\huge\boxed{\bf sec^4A(1- sin^4A)-2tan^2A=1}$

Additional Information

→  secA is 1/cosA

→  sinA/cosA is tanA

→  tan⁴A is (tan²A)²

→  sec⁴A is (sec²A)²

→  (A² - B²) is (A+B)(A-B)

→  sec²A - tan²A = 1