Assignment -1
Grade Class 12
Question:
<p><strong>Assertion (A): </strong>Domain of <span class="math-tex">\({y}=\cos ^{-1}(x)\)</span> is <span class="math-tex">\([-1,1]\)</span>.<br />
<strong>Reason (R):</strong> The range of the principal value branch of <span class="math-tex">\({y}=\cos ^{-1}(x)\)</span> is <span class="math-tex">\([0, \pi]-\left\{\frac{\pi}{2}\right\}\)</span>.</p>
<p style="display:inline">Both A and R are true and R is the correct explanation of A.</p>
<p style="display:inline">Both A and R are true but R is not the correct explanation of A.</p>
<p style="display:inline">A is true but R is false.</p>
<p style="display:inline">A is false but R is true.</p>
Step-by-Step Solution
Key Concept: Mastering the specific definitions of domains and principal value ranges for each inverse trigonometric function is essential for validating their mathematical properties.
<p>A is true but R is false.</p>
Correct Answer: C