Trigonometry & Inverse Trigonometry
Trigonometric Identities
Grade 11
Question:
<p>Find the value of \(\sin 20° + \cos 40° + \sin 50° + \tan 70° + \cot 80°\).</p>
<p>(a) \(\frac{4\sqrt{3}-1}{2}\)</p>
<p>(b) \(\frac{4}{2\sqrt{3}}\)</p>
<p>(c) \(\frac{4+\sqrt{3}}{2}\)</p>
<p>(d) other</p>
Step-by-Step Solution
Key Concept: Use complementary angle relationships and periodicity of trigonometric functions.
<p><strong>Solution:</strong></p><p>\(\sin 120° + \cos 240° + \sin 300° + \tan 420° + \cot 480°\)</p><p>\(= \frac{\sqrt{3}}{2} + \left(-\frac{1}{2}\right) + \left(-\frac{\sqrt{3}}{2}\right) + \sqrt{3} + \frac{1}{\sqrt{3}}\)</p><p>\(= \frac{\sqrt{3} - 1 - \sqrt{3} + 2\sqrt{3}}{2\sqrt{3}} = \frac{4+\sqrt{3}}{2\sqrt{3}}\)</p>
Correct Answer: B