turkey-yks 2023 Q27

turkey-yks · Other · yks-ayt Trig Proofs Ordering or Comparing Trigonometric Expressions
Let $a \in \left(\frac{3\pi}{4}, \pi\right)$,
$$\begin{aligned} & x = \sin(2a) \cdot \tan(a) \\ & y = \cos(2a) \cdot \cot(2a) \\ & z = \sin(a) \cdot \cot(2a) \end{aligned}$$
Given these equalities.
Accordingly, what are the signs of $\mathbf{x}$, $y$ and $\mathbf{z}$ respectively?
A) $+, +, -$ B) $+, -, -$ C) $-, -, -$ D) $-, +, +$ E) $-, -, +$
Let $a \in \left(\frac{3\pi}{4}, \pi\right)$,

$$\begin{aligned}
& x = \sin(2a) \cdot \tan(a) \\
& y = \cos(2a) \cdot \cot(2a) \\
& z = \sin(a) \cdot \cot(2a)
\end{aligned}$$

Given these equalities.

Accordingly, what are the signs of $\mathbf{x}$, $y$ and $\mathbf{z}$ respectively?

A) $+, +, -$
B) $+, -, -$
C) $-, -, -$
D) $-, +, +$
E) $-, -, +$