The value of cos 0-cos-7-cos2 -7-cos3 -7-cos4 -7-cos5 -7-cos6 -7 is

Cos 0+cosπ7+cos2π7+cos3π7+cos4π7+cos5π7+cos6π7 =1+(cosπ7+cos6π7)+(cos2π7+cos5π7) +(cos3π7+cos4π7) =1+(cosπ7+cos(π π7)) +(cos2π7+cos(π 2π7)) +(cos3π7+c ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

The value of ...

Question

The value of
$cos 0 + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}$ is

Open in App

Solution

$cos 0 + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} = 1 + (cos \frac{π}{7} + cos \frac{6 π}{7}) + (cos \frac{2 π}{7} + cos \frac{5 π}{7}) + (cos \frac{3 π}{7} + cos \frac{4 π}{7})$
$= 1 + (cos \frac{π}{7} + cos (π - \frac{π}{7})) + (cos \frac{2 π}{7} + cos (π - \frac{2 π}{7})) + (cos \frac{3 π}{7} + cos (π - \frac{3 π}{7}))$
$= 1 + 0 + 0 + 0 = 1$

Suggest Corrections

Similar questions

cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} =

Q. Simplify the following expression:

cos 0 + cos \frac{π}{2} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}

cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7} + cos \frac{7 π}{7} =

Q. Match the column

	List I		List II
A.	$cos 20^{\circ} + cos 80^{\circ} - \sqrt{3} cos 50^{\circ}$	1.	$- 1$
B.	$cos 0^{\circ} + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}$	2.	$- \frac{3}{4}$
C.	$cos 20^{\circ} + cos 40^{\circ} + cos 60^{\circ} + 4 cos 10^{\circ} cos 20^{\circ} cos 30^{\circ}$	3.	$1$
D.	$cos 20^{\circ} cos 100^{\circ} + cos 100^{\circ} cos 140^{\circ} - cos 140^{\circ} cos 200^{\circ}$	4.	$0$

cos \frac{2 π}{7} + cos \frac{4 π}{7} + cos \frac{6 π}{7}

Join BYJU'S Learning Program

Explore more

Sign of Trigonometric Ratios in Different Quadrants

Standard XII Mathematics

Join BYJU'S Learning Program

The value of cos0+cosπ7+cos2π7+cos3π7+cos4π7+cos5π7+cos6π7 is

cos0+cosπ7+cos2π7+cos3π7+cos4π7+cos5π7+cos6π7=1+(cosπ7+cos6π7)+(cos2π7+cos5π7) +(cos3π7+cos4π7) =1+(cosπ7+cos(π−π7)) +(cos2π7+cos(π−2π7)) +(cos3π7+cos(π−3π7)) =1+0+0+0=1

The value of
$cos 0 + cos \frac{π}{7} + cos \frac{2 π}{7} + cos \frac{3 π}{7} + cos \frac{4 π}{7} + cos \frac{5 π}{7} + cos \frac{6 π}{7}$ is