Question:
If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta \\ \end{matrix} \right] \) and \( AB = 1 \), then
\[
(\cos \theta)B
\]
is equal to
If \( A(\theta) = \left[ \begin{matrix} 1 & -\tan \theta \\ \end{matrix} \right] \) and \( AB = 1 \), then
\[
(\cos \theta)B
\]
is equal to
Show Hint
When manipulating trigonometric matrices, use angle addition or subtraction formulas to simplify the expressions.
Updated On: Jan 6, 2026
- \( A(\theta) \)
- \( A(\theta/2) \)
- \( A(-\theta) \)
- \( A(\theta/2) \)
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The Correct Option is C
Solution and Explanation
Step 1: Apply the angle formula.
We use the given expressions and properties of trigonometric functions to find the value of \( (\cos \theta)B \). The answer is \( A(-\theta) \).
Step 2: Conclusion.
Thus, the correct answer is option (C).
Final Answer: \[ \boxed{\text{(C) } A(-\theta)} \]
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