Penjelasan dengan langkah-langkah:

a. cos £ /(sec £ - tan £) = cos £ / (1/cos £ - sin £/cos £)

= cos £ x cos £/(1 - sin £)

= cos² £ / (1 - sin £)

= (1 - sin² £)/(1 - sin £)

= (1 + sin £)(1 - sin £)/(1 - sin £)

= 1 + sin £ (terbukti)

b. (1 + cos £ - sin² £)/(sec £ (1 + cos £))

= (1 + cos £ - (1 - cos² £))/(sec £ (1 + cos £))

= (cos £ + cos² £) /(sec £ (1 + cos £)

= cos £ (1 + cos £)/(sec £ (1 + cos £)

= cos £/sec £

= cos² £ (tidak terbukti)

d. (sec £ + tan £)² = sec² £ + 2 sec £ tan £ + tan² £

= sec² £ + (2 . 1/cos £ . sin £/cos £) + sec² £ - 1

= 2 sec² £ + 2 sin £ sec² £ - 1

= 2 sec² £ (1 + sin £) - 1

= (2/cos² £)(1 + sin £) - 1

= 2 (1 + sin £)/(1 - sin² £) - (1 - sin² £)/(1 - sin² £)

= (2 + 2 sin £ - 1 + sin² £)/(1 - sin² £)

= (sin² £ + 2 sin £ + 1)/(1 + sin £)(1 - sin £)

= (1 + sin £)²/(1 + sin £)(1 - sin £)

= (1 + sin £)/(1 - sin £) (terbukti)

i. 2/(1 - cosec £ + tan £)

= (belum terbukti)