Sederhanakan trigonometri tan a/sec a-1 + tan a/sec a+1

{(tan a)/(sec a - 1)} / {(tan a)/(sec a+ 1)}
perhatikan
a/b + c/d = (ad + bc) / bd
maka
{tan a(sec a + 1) + tan a(sec a - 1)} / {(sec a - 1)(sec a + 1)
= {tan a(sec a + 1 + sec a - 1)} / (sec²a - 1)
= {tan a(2.sec a)} / tan²a
= 2.sec a / tan²a
= 2(1/cos a) / (sin²a/cos²a)
= 2(1/cos a) × (cos²a/sin²a)
= 2.cos a / sin²a
= 2.cos a.cosec²a