Matrices & Determinants
Determinants
Grade Class 12
Question:
<p>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|" open="|"><mtable><mtr><mtd><msup><mi>sin</mi><mn>2</mn></msup><mn>2</mn><mi>x</mi></mtd><mtd><mi>cos</mi><mn>2</mn><mi>x</mi></mtd><mtd><mn>4</mn><msup><mi>sin</mi><mn>2</mn></msup><mfrac><mi>x</mi><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><msup><mi>tan</mi><mn>2</mn></msup><mfrac><mi>x</mi><mn>2</mn></mfrac></mtd><mtd><msup><mi>cos</mi><mn>2</mn></msup><mi>x</mi></mtd><mtd><mo>-</mo><msup><mi>sin</mi><mn>2</mn></msup><mi>x</mi></mtd></mtr><mtr><mtd><mo>-</mo><mn>2</mn><mi>cos</mi><mn>4</mn><mi>x</mi></mtd><mtd><msup><mi>tan</mi><mn>2</mn></msup><mfrac><mi>x</mi><mn>2</mn></mfrac></mtd><mtd><mi>sin</mi><mn>4</mn><mi>x</mi></mtd></mtr></mtable></mfenced></math> = a<sub>0</sub> + a<sub>1</sub>(cosx) + a<sub>2</sub>(cos<sup>2</sup>x) + ........ + a<sub>n</sub>(cos<sup>n</sup> x), then a<sub>0</sub> is -</p>
Step-by-Step Solution
Key Concept: Evaluate the determinant and compare coefficients or evaluate at a specific value of x.
The determinant evaluates to 0.
Correct Answer: 0