Inverse Trigonometric Functions
Nested Operations
Premium Question
Grade 12

Question:

The value of $\sin(\cot^{-1}(\cos(\tan^{-1} 1)))$ is:
(1) $\sqrt{\frac{2}{3}}$
(2) $\sqrt{\frac{1}{3}}$
(3) $\sqrt{\frac{3}{4}}$
(4) $\frac{1}{\sqrt{2}}$

Step-by-Step Solution

Key Concept: Evaluate step by step: $\tan^{-1}(1) = \pi/4, \cos(\pi/4) = 1/\sqrt{2}$. For $\cot^{-1}(1/\sqrt{2})$, draw a right triangle with $\cot \theta = 1/\sqrt{2}$ and read off $\sin \theta$.
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Correct Answer: (1)

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