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TRIGONOMETRIC FUNCTIONS — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSTRIGONOMETRIC FUNCTIONS1 Mark
MCQ
$\cos35^\circ+\cos85^\circ+\cos155^\circ=$
  • ✓
    $0$
  • B
    $\frac{1}{\sqrt3}$
  • C
    $\frac{1}{\sqrt2}$
  • D
    $\cos275^\circ$
✓

Answer

Correct option: A.
$0$
$\cos35^\circ+\cos85^\circ+\cos155^\circ$
$=\ 2\cos\Big(\frac{35^\circ+85^\circ}{2}\Big)\cos\Big(\frac{35^\circ-85^\circ}{2}\Big)+\cos155^\circ$ $\Big[\because\ \cos\text{A}+\cos\text{B}=2\cos\Big(\frac{\text{A+B}}{2}\Big)\cos\Big(\frac{\text{A}-\text{B}}{2}\Big)\Big]$
$=\ 2\cos60^\circ\cos(-25^\circ)+\cos155^\circ$
$=\ 2\times\frac{1}{2}\cos25^\circ+\cos155^\circ$
$=\ \cos25^\circ+\cos155^\circ$
$=\ 2\cos\Big(\frac{25^\circ+155^\circ}{2}\Big)\cos\Big(\frac{25^\circ-155^\circ}{2}\Big)$
$=\ 2\cos90^\circ\cos65^\circ$
$=\ 0$

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