taiwan-gsat 2020 Q1

taiwan-gsat · Other · ast__math-a 6 marks Trig Proofs Ordering or Comparing Trigonometric Expressions

Given $45^{\circ} < \theta < 50^{\circ}$, and let $a = 1 - \cos^{2}\theta$, $b = \frac{1}{\cos\theta} - \cos\theta$, $c = \frac{\tan\theta}{\tan^{2}\theta + 1}$. Regarding the relative sizes of the three values $a$, $b$, $c$, select the correct option.
(1) $a < b < c$
(2) $a < c < b$
(3) $b < a < c$
(4) $b < c < a$
(5) $c < a < b$

Given $45^{\circ} < \theta < 50^{\circ}$, and let $a = 1 - \cos^{2}\theta$, $b = \frac{1}{\cos\theta} - \cos\theta$, $c = \frac{\tan\theta}{\tan^{2}\theta + 1}$. Regarding the relative sizes of the three values $a$, $b$, $c$, select the correct option.\\
(1) $a < b < c$\\
(2) $a < c < b$\\
(3) $b < a < c$\\
(4) $b < c < a$\\
(5) $c < a < b$

Paper Questions

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