Question

sec^2 a(sec^2 a -2) +1 =tan^4 a

Answer 1

Answer:

Step-by-step explanation:

Given :

sec² A (sec²A - 2) + 1 = tan⁴ A

Solution :

We know that,

sec² A - tan² A = 1

⇒ sec² A = tan² A + 1

______

Proof :

LHS ⇒ sec² A (sec²A - 2) + 1

⇒ (tan² A + 1) [(tan²A + 1) - 2] + 1  

⇒ (tan² A + 1) [tan²A - 1] + 1

⇒ [tan⁴A - 1] + 1

⇒ tan⁴A = RHS

Hence proved,.