Trigonometry & Inverse Trigonometry
Trigonometric Identities
Grade 11
Question:
<p>The value of \(\cos^2 10° - \cos 10° \cos 50° + \cos^2 50°\) is</p>
<p>(a) \(\frac{3}{2}(1 + \cos 20°)\)</p>
<p>(b) \(\frac{3}{4} + \cos 20°\)</p>
<p>(c) \(\frac{3}{2}\)</p>
<p>(d) \(\frac{3}{4}\)</p>
Step-by-Step Solution
Key Concept: Use complementary angle relations and trigonometric identities to simplify the expression.
<p>Use the complementary angle relation $\cos 50° = \sin 40°$ and product-to-sum formulas. Alternatively, let $a = \cos 10°$ and $b = \cos 50°$ and evaluate the quadratic form.</p>
Correct Answer: D