Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p><strong>Ex. 36.</strong> Match the statements of Column I with the values of Column II.</p><p><strong>Column I:</strong></p><p><strong>(A)</strong> The number of solutions of the equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>|</mo><mi>tan</mi><mn>2</mn><mi>x</mi><mo>|</mo><mo>=</mo><mi>sin</mi><mi>x</mi></mrow></math>; <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>]</mo></math></p>
Step-by-Step Solution
Key Concept: Solve trigonometric equations graphically by finding intersection points of the two curves.
<p><strong>Solution:</strong></p><p>The number of solutions of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>|</mo><mi>tan</mi><mn>2</mn><mi>x</mi><mo>|</mo><mo>=</mo><mi>sin</mi><mi>x</mi></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>[</mo><mn>0</mn><mo>,</mo><mi>π</mi><mo>]</mo></math> are 4.</p><p>This is found by graphical intersection of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>y</mi><mo>=</mo><mo>|</mo><mi>tan</mi><mn>2</mn><mi>x</mi><mo>|</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>y</mi><mo>=</mo><mi>sin</mi><mi>x</mi></mrow></math>.</p>
Correct Answer: A→q