If \(\sin(90^\circ - x) = \cos(2x)\), then what is x?
0°
Step 1 – Co-function identity: \(\sin(90^\circ - x) = \cos x\). So \(\cos x = \cos(2x)\).
Step 2 – Solve: \(\cos x = \cos(2x) \implies 2x = \pm x + 360^\circ k\). Taking \(2x = -x \implies 3x = 0 \implies x = 0^\circ\) (within the principal range and matching the options).
Verify: \(\sin 90^\circ = 1\), \(\cos 0 = 1\) ✓.
Hence, the correct answer is 0°.
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