Question Number 114682 by 175mohamed last updated on 20/Sep/20

Answered by mindispower last updated on 20/Sep/20

∀k∈[2,n] tg(a_k )−tg(a_(k−1) )=((sin(a_k ))/(cos(a_k )))−((sin(a_(k−1) ))/(cos(a_(k−1) ))) =sin(a_k −a_(k−1) )sec(a_k )sec(a_(k−1) ) =sin(d)sec(a_k )sec(a_(k−1) ) ⇔((tg(a_k )−tg(a_(k−1) ))/(sin(d)))=sec(a_k )sec(a_(k−1) ) Σ_(k=2) ^n ((tg(a_k )−tg(a_(k−1) ))/(sin(d)))=Σ_(k=2) ^n sec(a_k )sec(a_(k−1) ) ⇔((tg(a_n )−tg(a_1 ))/(sin(d)))=sec(a_1 )sec(a_2 )+ sec(a_2 )sec(a_3 )+...+sec(a_(n−1) )sec(a_n )