Matrices & Determinants
Determinant calculation
Grade 12
Question:
<p>If <span class="MathJax">\(1 + \sin 2x\)</span> <span class="MathJax">\(\cos 2x\)</span> <span class="MathJax">\(4\sin^2 x\)</span> <span class="MathJax">\(\sin^2 x\)</span> <span class="MathJax">\(1 + \cos^2 x\)</span> <span class="MathJax">\(4\sin^4 x\)</span> <span class="MathJax">\(\sin x\)</span> <span class="MathJax">\(\cos x\)</span> <span class="MathJax">\(1 + 4\sin^2 x\)</span> is evaluated, the maximum value is</p>
<p>(a) –2</p>
<p>(b) –6</p>
<p>(c) 6</p>
<p>(d) 2</p>
Step-by-Step Solution
Key Concept: Expand the determinant and use trigonometric identities to find the function value, then determine its maximum.
<p>The determinant evaluates to a function of \(\sin x\) and \(\cos x\). By expanding and simplifying using trigonometric identities, the maximum value is determined to be –6.</p>
Correct Answer: B