Answer :

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 a^{6}-b^{6}

a^{6}-b^{6} = (a + b)(a-b)(a^{2} + b^{2} + ab)(a^{2} + b^{2}-ab)

Therefore (sec x)^{6} -1^{6} = (sec x + 1)(sec x-1)(sec^{2}x + 1 + sec x)(sec^{2}x + 1-sec x)

(sec x)^{6} -1^{6} = (sec x + 1)(sec x-1)(1 + sec^{2}x + sec^{4}x)

S = = (sec x + 1)(1 + sec^{2}x + sec^{4}x)

So the correct answer is option B.

Rate this question :

The fifth term ofTamil Nadu Board - Math

Find out which ofTamil Nadu Board - Math

Which term of theTamil Nadu Board - Math

If aTamil Nadu Board - Math

A company purchasTamil Nadu Board - Math

If ₹1000 is deposTamil Nadu Board - Math

If the third termTamil Nadu Board - Math

The common ratio Tamil Nadu Board - Math

If xTamil Nadu Board - Math

If the product ofTamil Nadu Board - Math