Exams › SSC CGL (Prelims) › General

If \(\tan(4x+15^\circ)=\cot(3x-16^\circ)\), find \(x\).

1. 11°
2. 12°
3. 13°
4. 14°

Correct answer: 13°

Solution

Using \(\cot \theta=\tan(90^\circ-\theta)\), we get \(\tan(4x+15^\circ)=\tan(90^\circ-(3x-16^\circ))=\tan(106^\circ-3x)\). Taking the principal acute-angle relation, \(4x+15=106-3x\), so \(7x=91\) and \(x=13^\circ\).

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