iran-konkur 2021 Q105

iran-konkur · Other · konkur-riazi_1400_specialized Addition & Double Angle Formulae Half-Angle Formula Evaluation
105- If $\tan\!\left(\dfrac{\alpha}{2}\right) = \dfrac{1}{4}$, what is the value of $\dfrac{\tan(\alpha) - \sin(\alpha)}{\sin(\alpha) - \cos(\alpha)}$?
(1) $-\dfrac{91}{105}$ (2) $-\dfrac{19}{105}$ (3) $\dfrac{16}{105}$ (4) $\dfrac{91}{105}$
\textbf{105-} If $\tan\!\left(\dfrac{\alpha}{2}\right) = \dfrac{1}{4}$, what is the value of $\dfrac{\tan(\alpha) - \sin(\alpha)}{\sin(\alpha) - \cos(\alpha)}$?

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(1) $-\dfrac{91}{105}$ \hfill (2) $-\dfrac{19}{105}$ \hfill (3) $\dfrac{16}{105}$ \hfill (4) $\dfrac{91}{105}$

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