Q. 175.0( 1 Vote )
If x 0, then 1 + sec x + sec2x + sec3x + sec4x + sec5x is equal to
A. (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.
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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