Question

sec6 x - tan6 x = 1 + 3 tan2 x + 3 tan4 x.
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Answer 1

Step-by-step explanation:

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

= (sec^2-tan^2)^3+3sec^2*tan^2 (sec^2-tan^2)

= (1)^3+3 (1+tan^2x)tan^2x (1)

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

=1+3 (tan^2x+tan^4x)

=1+3tan^2x+3tan^4x

=RHS