Question

sec^6 a - tan^6 a - 3 sec^2a tan^2 a =1​

Answer 1

Answer:

Answer is 1.

Step-by-step explanation:

sec^6a - tan^6a - 3 sec^2a tan^2a

= (sec^2a)^3 - (tan^2a)^3 - 3 sec^2a tan^2a

( x^3 - y^3 = (x - y)(x^2 + y^2 + xy)

= ( sec^2a - tan^2a)(sec^4a + tan^4a + sec^2a tan^2a) - 3 sec^2a tan^2a

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

= sec^4a + tan^4a + sec^2a tan^2a - 3 sec^2a tan^2a

= sec^4a + tan^4a - 2 sec^2a tan^2a

= (sec^2a - tan^2a)^2

=1  Ans....