Bentuk sederhana dari tanA/sec-1 + tanA/sec+1 adalah?

Bab Trigonometri
Matematika SMA Kelas X

tan A /(sec A + 1) + tan A /(sec A - 1)
= (tan A . (sec A + 1) + tan A . sec A - 1)) / (sec² A - 1)
= (tan A . (sec A + 1 + sec A - 1)) / tan² A
= 2 sec A / tan A
= 2 . (1/cos A) . cos A/sin A
= 2 / sin A
= 2 cosec A

[tex]\displaystyle TRIGONOMETRI \\ \\ = \frac{tan \ A}{sec \ A - 1} + \frac{tan \ A}{sec \ A + 1} \\ = \frac{tan \ A . sec \ A + tan \ A + tan \ A . sec \ A - tan \ A}{sec^{2} \ A - 1} \\ = \frac{2 \ tan \ A \ sec \ A}{tan^{2} \ A} \\ = \frac{2 \ sec \ A}{tan \ A} \\ = \frac{2}{cos \ A . \frac{sin \ A}{cos \ A} } \\ = \frac{2}{sin \ A} \\ = 2 \ csc \ A \ -\ \textgreater \ \ Jawab [/tex]