Question

Prove that:- Sec^4A (1-Sin^4A) - 2tan^2A = 1

Answer 1

Step-by-step explanation:

LHS = sec^4 A ( 1- sin^4 A ) -2 tan²A

= sec^4 A - ( sin^4A/cos^4A) - 2 tan² A

= sec^4 A - tan^4 A -2tan²A

= ( tan²A+1)² - tan^4A - 2 tan²A

= tan^4 A +2tan²A+1 - tan^4 A -2tan²A

= 1

= RHS