CBSE BoardEnglish MediumSTD 10MathsTrigonometric Ratios3 Marks
Question
Write the value of $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ.$
✓
Answer
Given that: $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos89^\circ\cos90^\circ\cos91^\circ\dots\cos179^\circ$
$=\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos89^\circ\times0\dots\cos179^\circ\cos180^\circ$
$=0$ $\big[\cos90^\circ=0\big]$
Hence the value of $\cos1^\circ\cos2^\circ\cos3^\circ\dots\cos179^\circ\cos180^\circ\text{ is }0$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.