If t=\cos 79^{\circ}, then what is \csc 79^{\circ}(1-\cos 79^{\circ}) equal to?
- A. \sqrt{\frac{1+t}{1-t}}
- B. \frac{t}{\sqrt{1-t^{2}}}
- C. \frac{\sqrt{1-t^{2}}}{t}
- D. \sqrt{\frac{1-t}{1+t}} ✓
Correct Answer: D. \sqrt{\frac{1-t}{1+t}}
Explanation
\csc \theta (1-\cos \theta) = \frac{1-\cos \theta}{\sin \theta}. Substitute \cos \theta = t and \sin \theta = \sqrt{1-t^2} to get \frac{1-t}{\sqrt{(1-t)(1+t)}} = \sqrt{\frac{1-t}{1+t}}.
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