Q. 175.0( 1 Vote )

# If x 0, then 1 + sec x + sec2x + sec3x + sec4x + sec5x is equal toA. (1 sec x) (sec2x + sec3x + sec4x)B. (1 + sec x) (1 + sec2x + sec4x)C. (1 sec x) (sec x + sec3x + sec5x)D. (1 + sec x) (1 + sec3x + sec4x)

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.

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