Question

sec⁴A (1-sin⁴A) -2tan²A=1

Answer 1

solution:

$sec^4A(1-sin^4a)2tan^4A\\</p><p>=sec^4A-sec^4Asin^4A-2sin^2A\\</p><p>=sec^4A-sin^4(\frac{1}{cos^4A})-2tan^2A\\</p><p>=sec^4A-tan^4A-2tan^2A\\</p><p>={(sec^2A)^2-(tan^2A)^2}-2tan^2A\\</p><p>=(sec^2A+tan^2A)(sec^2A-tan^2A)-2tan^2A\\</p><p>=sec^2A+tan^2A-2tan^2A\\</p><p>\because sec^2A-tan^2A=1\\</p><p>=sec^2A-tan^2A</p><p>=1(proved.)$