Inverse Trigonometric Functions
NCERT Class 12
CBSE
Grade 12
Question:
Solve for $x$: $\cos(\tan^{-1} x) = \sin\left(\cot^{-1} \dfrac{3}{4}\right)$.
Step-by-Step Solution
RHS $= 4/5$, LHS $= 1/\sqrt{1+x^2}$. [1.5 Marks]
$1/\sqrt{1+x^2} = 4/5 \Rightarrow 1+x^2 = 25/16 \Rightarrow x^2 = 9/16 \Rightarrow x = \pm 3/4$. [1.5 Marks]
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🎯 Official CBSE Marking Scheme:
Evaluating RHS $= 4/5$ and LHS $= 1/\sqrt{1+x^2}$: 1.5 Marks
Solving $x = \pm 3/4$: 1.5 Marks
Correct Answer:
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