If x 0, then 1 + sec x + sec²x + sec³x + sec⁴x + sec⁵x is equal to

We see that the problem under consideration is a GP with a = 1 and common ratio r = sec x.

Sum of GP S =

Where n = number of terms, here n = 6.

Therefore

S =

The numerator is of the form a⁶-b⁶

a⁶-b⁶ = (a + b)(a-b)(a² + b² + ab)(a² + b²-ab)

Therefore (sec x)⁶ -1⁶ = (sec x + 1)(sec x-1)(sec²x + 1 + sec x)(sec²x + 1-sec x)

(sec x)⁶ -1⁶ = (sec x + 1)(sec x-1)(1 + sec²x + sec⁴x)

S = = (sec x + 1)(1 + sec²x + sec⁴x)

So the correct answer is option B.