Question

please answer the question ​

Answer 1

hey there

refer to attachment

Answer 2

- > 3rd option....

Here , if we look at the question , first of all take a sin(π/6) at numerator and denominator for our convenience to transform the numerator into the trignometic equation , which we can further operate the terms with denominator.

2 is a constant so take it out side the summition then use sin(A-B) formula , after that we can cancel out the some terms of numerator by denominator , finally we get { cot [ (π/4)+ [(k-1)π/6] ] - cot [(π/4)+(kπ/6)] } .

Now , Expand the series upto k=1 to 13 , cancel out the terms . after that perform s operations using trignometic identies and mesurements of angles , Hence we get our answer 2 (√3 - 1 ).