Question

sec^4A(1-sin^4A)-2tan^2A=1
PROVE THIS PLZ

Answer 1

Trigonometry,

We have,
sec⁴A(1 - sin⁴A) - 2tan²A = 1

Now,
LHS = sec⁴A(1 - sin⁴A) - 2tan²A [ using the formula a² - b² = (a + b) (a - b)]

= 1/cos⁴A(1 - sin²A)(1 + sin²A) - 2tan²A

= 1/cos⁴A × cos²A × (2 - cos²A) - 2tan²A

= 1/cos²A × (2 - cos²A) - 2tan²A

= 2/cos²A - 1 - 2tan²A

= 2sec²A - 2tan²A - 1

= 2(sec²A - tan²A) - 1 [ As we konw that sec²A - tan²A = 1 ]

= 2 × 1 - 1

= 1 = RHS

That's it
Hope it helped ( ･ั﹏･ั)