$c o s 35^{\circ} + c o s 85^{\circ} + c o s 155^{\circ} =$

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

$\frac{1}{\sqrt{3}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$\frac{1}{\sqrt{2}}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

$c o s 275^{\circ}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
0

$c o s 35^{\circ} + c o s 85^{\circ} + c o s 155^{\circ} = = 2 c o s (\frac{35^{\circ} + 85^{\circ}}{2}) c o s (\frac{35^{\circ} - 85^{\circ}}{2}) + c o s 155^{\circ} [∵ c o s A + c o s B = 2 c o s (\frac{A + B}{2}) c o s (\frac{A - B}{2})] = 2 c o s 60^{\circ} c o s (- 25^{\circ}) + c o s 155^{\circ} = 2 \times \frac{1}{2} c o s 25^{\circ} + c o s 155^{\circ} = c o s 25^{\circ} + c o s 155^{\circ} = 2 c o s (\frac{25^{\circ} + 155^{\circ}}{2}) c o s (\frac{25^{\circ} - 155^{\circ}}{2}) = 2 c o s 90^{\circ} c o s 65^{\circ} = 0$

Suggest Corrections

104

Similar questions

\frac{1}{\sqrt{3}}

\frac{1}{\sqrt{2}}

sin 70^{\circ} sin 50^{\circ} - cos 85^{\circ} cos 65^{\circ} =

Value of cos35⁰cos45⁰ is

\frac{cos 35}{sin 55} + \frac{tan 27 tan 63}{sin 30} - 3 (tan 60)^{2}

Show that :
(i) $\sin 50 ° \cos 85 ° = \frac{1 - \sqrt{2} \sin 35 °}{2 \sqrt{2}}$

(ii) $\sin 25 ° \cos 115 ° = \frac{1}{2} (\sin 140 ° - 1)$

Join BYJU'S Learning Program