Trigonometry & Inverse Trigonometry
Trigonometric Identities
Grade 11
Question:
<p>Suppose that <span>\(a\)</span> is a non-zero real number for which <span>\(\sin x + \sin y = a\)</span> and <span>\(\cos x + \cos y = 2a\)</span>. The value of <span>\(\cos(x - y)\)</span> is</p>
<p>(a) <span>\(\frac{4}{3a^2 - 2}\)</span></p>
<p>(b) <span>\(\frac{9a^2 - 2}{2}\)</span></p>
<p>(c) <span>\(\frac{9a^2 - 2}{2}\)</span></p>
<p>(d) <span>\(\frac{5a^2 - 2}{2}\)</span></p>
Step-by-Step Solution
Key Concept: Square both given equations and add them, then use <span>\(\cos(x-y) = \cos x \cos y + \sin x \sin y\)</span>.
<p>Solution not provided in the text.</p>
Correct Answer: C