Trigonometry & Inverse Trigonometry
Trigonometric Equations
Grade 11
Question:
<p>The possible value(s) of <span class="math">\theta</span> satisfying the equation <span class="math">\sin 2\theta \tan\theta + \cos 2\theta \cot\theta - \sin 2\theta = 1 + \tan\theta + \cot\theta</span> where <span class="math">\theta \in [0, \pi]</span> is/are:</p>
<p>(a) <span class="math">\frac{\pi}{4}</span></p>
<p>(b) <span class="math">\pi</span></p>
<p>(c) <span class="math">\frac{7\pi}{12}</span></p>
<p>(d) None of these</p>
Step-by-Step Solution
Key Concept: Convert all trigonometric functions to sine and cosine, then simplify and solve the resulting polynomial or trigonometric equation.
<p><strong>Solution:</strong> Rearrange the equation and simplify using trigonometric identities. Express all terms in terms of <span class="math">\sin\theta</span> and <span class="math">\cos\theta</span>. Solve the resulting equation and verify which solutions lie in the interval <span class="math">\theta \in [0, \pi]</span>.</p><p>∴ Answer is (c).</p>
Correct Answer: C