Symmetric Properties and Pythagorean Identity - Questions

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Question 1

19211

Given that \(0 < x < \dfrac{\pi }{2}\) and \(\cos x = \sin \dfrac{\pi }{3}\), find the value of \(x\)

Answer

\(\dfrac{\pi }{6}\)

Worked Solution

\begin{align}
\cos x=\sin \left(\frac{\pi}{2}-x\right) &=\sin \frac{\pi}{3} \\
\therefore \frac{\pi}{2}-x &=\frac{\pi}{3} \\
x &=\frac{\pi}{6}
\end{align}

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