Question

sec
${sec}^{6} - {tan}^{6} = 1 + 3 \times {tan}^{2} - {sec}^{2}$
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Answer 1

Answer:

1+3 sec^2x tan^2x

Step-by-step explanation:

sec^6x-tan^6=(sec^2x)^3-(tan^2x)^3

=(sec^2x-tan^2x) (sec^4x + sec^2x tan^2x tan^4x)

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

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

=sec^2x- tan^2x + sec^2x tan^2x + 2sec^2x tan^2x

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