Assignment -1
Grade Class 12
Question:
<p>The principal value of cos<sup>-1 </sup><span class="math-tex">\(\left(\frac{\sqrt{3}}{2}\right)\)</span> is</p>
<p style="display:inline"><span class="math-tex">\(\frac{5\pi}{6}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{\pi}{6}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{8\pi}{6}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{7\pi}{6}\)</span></p>
Step-by-Step Solution
Key Concept: To find the principal value, equate the inverse cosine expression to a variable and solve the resulting trigonometric equation by identifying the corresponding standard angle.
<p>Let the principle value be given by x<br />
Now, let x = cos<sup>-1</sup><span class="math-tex">$\left(\frac{\sqrt{3}}{2}\right)$</span><br />
<span class="math-tex">$\Rightarrow \cos x=\frac{\sqrt{3}}{2}$</span><br />
<span class="math-tex">$\Rightarrow$</span> cos x = cos <span class="math-tex">$\left(\frac{\pi}{6}\right)\left(\because \cos \left(\frac{\pi}{6}\right)=\frac{\sqrt{3}}{2}\right)$</span><br />
<span class="math-tex">$\Rightarrow$</span> x = <span class="math-tex">$\frac{\pi}{6}$</span></p>
Correct Answer: B