Question

Find the number of 2-digit positive integer N such that tan^n 15⁰ + cot^n 15⁰ is an integer.​

Answer 1

Answer:

tan 15 + cot 15

= sin 15 / cos 15 + cos 15 / sin 15

= (sin²15 + cos²15) / (sin 15 cos 15)

= 1 / (1/2 sin 30)

= 2 / sin 30

= 2 / (1 / 2)

= 4