Assignment -1
Grade Class 12
Question:
<p>if <span class="math-tex">\(\theta = co{s^{- 1}}\left( {\frac{1}{x}} \right),\)</span> then tan θ is equal to</p>
<p style="display:inline"><span class="math-tex">\(\frac{{\sqrt {{x^2} - 1} }}{x}\)</span></p>
<p style="display:inline"><span class="math-tex">\(2\sqrt {{x^2} + 1} \)</span></p>
<p style="display:inline"><span class="math-tex">\(\sqrt {{x^2} - 1} \)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{{x\sqrt {1 - {x^2}} }}{{\left| x \right|}}\)</span></p>
Step-by-Step Solution
Key Concept: Use the definition of the given inverse trigonometric function to identify two sides of a right-angled triangle and find the third side using the Pythagorean theorem.
<p>if <span class="math-tex">\(\theta = {\cos ^{ - 1}}\left( {\frac{1}{x}} \right)\)</span></p>
<p><span class="math-tex">\( \Rightarrow \cos \theta = \frac{1}{x} = \frac{{Base}}{{Hyp.}} \Rightarrow \tan \theta = \frac{{Perp.}}{{Base}} = \frac{{\sqrt {{x^2} - 1} }}{x}\)</span></p>
Correct Answer: A