Trigonometry & Inverse Trigonometry
Double angle formula
Grade 11
Question:
<p>The value of \(\dfrac{1 - \tan^2 15°}{1 + \tan^2 15°}\) is</p>
<p>1</p>
<p>\(\dfrac{\sqrt{3}}{2}\)</p>
<p>\(\dfrac{\sqrt{3}}{2}\)</p>
<p>\(\dfrac{1}{2}\)</p>
Step-by-Step Solution
Key Concept: Recognize that the expression (1 - tan²θ)/(1 + tan²θ) is the double angle formula for cosine: cos(2θ) = (1 - tan²θ)/(1 + tan²θ). Therefore, the answer is cos(30°).
<p><strong>Step 1:</strong> Recognize the standard trigonometric identity.</p><p>We know that: cos(2θ) = (1 - tan²θ)/(1 + tan²θ)</p><p><strong>Step 2:</strong> Apply the formula with θ = 15°.</p><p>Therefore: (1 - tan²15°)/(1 + tan²15°) = cos(2 × 15°) = cos(30°)</p><p><strong>Step 3:</strong> Evaluate cos(30°).</p><p>cos(30°) = √3/2</p><p>∴ Answer: <strong>√3/2</strong> (Option B)</p>
Correct Answer: B