The value of cot 15° cot 10° cot 80° cot 75° cot 45° is

The correct answer is Option (4) → 1

For two angles that add up to 90°, \(\cot(90^\circ-\theta)=\tan\theta\), so \(\cot\theta\times\cot(90^\circ-\theta)=\cot\theta\times\tan\theta=1\). The angles are paired this way.

• 15° and 75° together make 90°, so \(\cot15^\circ\times\cot75^\circ=1\)

• 10° and 80° together make 90°, so \(\cot10^\circ\times\cot80^\circ=1\)

• The angle left over is 45°, and \(\cot45^\circ=1\)

• The whole product \(=1\times1\times1=1\)

Tip: When a product of tan or cot values is asked, look for pairs of angles adding up to 90°; each such pair gives 1.