If sin x = cos(2x - 10°), find the value of x.
33.33°
Given \(\sin x = \cos(2x-10°)\), using the identity \(\cos\theta = \sin(90°-\theta)\), we get \(\cos(2x-10°) = \sin(90°-(2x-10°)) = \sin(100°-2x)\).
So \(\sin x = \sin(100°-2x)\), which gives \(x = 100°-2x\).
Solving, \(3x = 100°\), so \(x = \frac{100°}{3} = 33.33°\).
Hence, the answer is 33.33°.
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