Question

C
Q1.Find the number of 2-digit positive integers N such that tanN15° + cot 15° is an integer

Answer 1

Step-by-step explanation:

*Given: Find the number of 2-digit positive integers N such that tanN15° + cotN15° is an integer.

To Find: Value of N.

Solution: We know that tan45°=1 and cot 45°=1.

Thus,

One have to assume N,such that tanN15° + cotN15° will become an integer.

Let N=15

$\begin{gathered} \tan(15 \times 15°) + \cot(15 \times 15°) \\ \\ = \tan(225°) + \cot(225° ) \\ \\ = \tan(180° + 45°) + \cot(180°+ 45°) \\ \end{gathered}$

we know that

$\begin{gathered}tan(180° + \theta) = tan \: \theta \\ \\ cot(180° + \theta) = cot \: \theta \\ \end{gathered}$

Thus,

$\begin{gathered} = \tan(45)° + \cot(45°) \\ \\ = 1 + 1 \\ \\ = 2 \: \in \: Z \end{gathered}$

Final answer:

For N=15

$\begin{gathered} \bold{\red{\tan(N15°) + \cot(N15°) = 2}} \\ \end{gathered}$

Hope it helps you.

Answer 2

15 will be answer as it will form 2 as a natural no