Inverse Trigonometric Functions
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Simplify $\cos^{-1}\left(\sqrt{\dfrac{1 + \cos x}{2}}\right)$, $0 < x < \pi$.
Step-by-Step Solution
$\\sqrt{\\dfrac{1+\\cos x}{2}} = \\cos(x/2)$. [1.5 Marks]
$\cos^{-1}(\cos(x/2)) = \dfrac{x}{2}$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Applying half-angle cosine identity: 1.5 Marks
Evaluating simplified form $= x/2$: 1.5 Marks
Correct Answer:
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